
Bosons  The Birds
That Flock and Sing Together
Dr V B Kamble
Never accept an idea as along as you, yourself, are not satisfied with its consistency and logical structure on which the concepts are based. Study the Masters. These are the people who had made significant contributions to the subject. Lesser authorities clearly bypass the difficult points  Satyendra Nath Bose
Exactly a hundred years after the first Nobel Prize for Physics was awarded to Wilhelm Conrad Rontgen (18451923) in 1901, the Nobel Prize for the year 2001 was jointly awarded to Eric A. Cornell (b.1961), Wolfgang Ketterle (b.1957) and Carl Wieman (b.1951) of the U.S.A. for the achievement of the BoseEinstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of such condensates. Indeed, BoseEinstein condensate is a new state of matter. The 2001 Nobel Laureates have succeeded in having caused atoms to sing in unison  somewhat similar to light photons, or the quanta of light in a laser beam which have the same energy and oscillate together. To cause matter also to behave in this controlled way has long been a challenge for researchers  this is precisely what they achieved in 1995. It all started in 1924 when the Indian physicist Satyendra Nath Bose made important theoretical calculations regarding the behaviour of light particles or photons as they are called. He sent his results to Einstein who extended the theory to a certain type of atoms. Einstein predicted that if a gas of such atoms were cooled to a very low temperature, all the atoms would suddenly gather in the lowest possible energy state. The process is similar to when drops of liquid form from a gas, hence the term condensation. However, seventy years were to pass before scientists succeeded in achieving this extreme state of matter. In this article, we shall briefly trace the great saga of the last seventy five years. We shall begin our story with Satyendra Nath Bose one of the makers of the Twentieth Century Physics. Satyendra Nath Bose Satyendra Nath BoseSatyendra Nath Bose (1894 1974) was born on the New Years Day, January 1, 1894, in Calcutta. His ancestral home was located in the village Bara Jagulia, in the District of Nadia, about 48km from Calcutta. Satyendra Nath was the only son and he had after him six sisters in succession. Satyendra Naths schooling began at the age of five. At first he was put in the Normal School, which was close to his home. Later on, when the family moved to their own house at Goabagan, he was admitted to the neighbouring New Indian School. In the final year of school, he was admitted to the Hindu School. He passed his entrance examination (matriculation) in 1909 and stood fifth in order of merit. He next joined the intermediate science course at the Presidency College, Calcutta, where he came under the tutelage of such illustrious teachers as Jagadis Chandra Bose and Prafulla Chandra Ray. Meghnad Saha came from Dacca (Now Dhaka) and joined the Presidency College two years later. P.C. Mahalanobis and Sisir Kumar Mitra were a few years senior to this group. Satyendra Nath Bose opted for Mixed Mathematics for his B.Sc.and passed the examinations standing first in 1913. The same result was repeated in the M.Sc. Mixed Mathematics examinations in 1915. It is said that the marks secured by Satyendra Nath Bose in his M.Sc. examination created a new record in the annals of the Calcutta University  which is yet to be surpassed! In 1914, at the age of twenty, Satyendra Nath Bose was married to Ushabati Ghosh, while she was only eleven. They had nine children. Two of them died in their infancy. In 1974, on his death, he left behind him his surviving widow, two sons and five daughters. Incidentally, both his sons studied engineering while most of his daughters had graduated before they were married. Satyendra Nath Bose was a scientist of varied interests and had an artistic bent of mind. Besides English, he was equally at home with French, German and Italian. Hugo, Goethe, Buddha and Sanskrit classes gave him inspiration and pleasure, while Rabindra Nath Tagores writings cast a spell over him. After his M.Sc., he joined the Calcutta University as a research scholar in 1916 and started his studies in the theory of relativity. Next year, both he and M.N. Saha were appointed lecturers in Physics and Applied Mathematics Department of the University College of Science, Calcutta. Indeed it was an exciting era in the history of scientific progress. The quantum theory had just appeared on the horizon and important results had started pouring in. Saha and Bose translated the original papers of Albert Einstein (18791955) and H. Minkowsky (18641909) from German into English which were brought out in the form of a booklet entitled The Principle of Relativity by the University. Bose joined the Dacca university, which was founded in 1921, as Reader in Physics. Bose had carefully studied Max Plancks book entitled Thermodynamik und Warmestrahlung. He knew about phase space and Boltzmann statistics from Gibbs book: Vorlesungen uber Gastheorie. He also knew about Einsteins deduction of Plancks formula and how he had never been satisfied with the derivation of this quantum law. Plancks condition ran counter to the classical ideas. Planck was aware of the difficulties, but he had never been able to resolve them. He wanted to reconcile his theory with the classical theory. Bose wanted to solve the difficulty in his own way. How he achieved this, we shall presently see. Albert Einstein During his visit to Europe, Bose met a number of giant figures of that time like Paul Langevin, Madam Curie, Maurice de Broglie (Brother of Louis Broglie, who proposed that matter could behave as a particle as well as wave). Bose returned to Dacca some time during the latter half 1926 where he joined as Professor. He remained there from 1926 to 1945. His interest shifted from one problem to another statistics, relativity and so on. He returned to Calcutta in 1945 to become the Khaira Professor of Physics in Calcutta University and stayed there till 1956. After a brief stint at Shantiniketan, he returned to Calcutta in 1958 when he was appointed National Professor. He held this position until his death 16 years later. In his later years he became actively interested in popularization of science and took to writing on and about science in Bengali. For this purpose he founded the Bangiya Bijnana Parishad (Science Association of Bengal). He was extremely fond of instrumental music and played on the Esraj like a master . He was made a Fellow of Royal Society of London in 1958. He was a Foundation Fellow of the Indian National Science Academy (1935). At a function to celebrate his eightieth birthday, he said, Well, after all, if one has lived through so many years of struggle, and if at the end he finds that his work has been appreciated, he feels that he does not need to live long. I think this is the faithful end to a long career. These words proved prophetic indeed. Only a few days later, he died on February 4, 1974. As a glowing tribute, the Department of Science and Technology, Government of India, in 1986 established the Satyendra Nath Bose National Centre for Basic Science in Calcutta.
The Crucial StepBose set about thinking deeply and spending sleepless nights about the radiation problem. Next he took the crucial step in the identification of blackbody radiation as a photon gas. He showed that the photons had a startling property of being strictly identical. This led to a new expression for the thermodynamic properties of an assembly of photons in contrast to what one would have calculated on the then accepted basis, the socalled MaxwellBoltzmann statistics. But with the revolution that Bose introduced into the counting process one obtains the correct thermodynamics of the photon gas. And that one step was the basis of a new synthesis between the wave and particle properties of photons; and, with it, the foundation of quantum field theory. Bose communicated this paper to the Philosophical Magazine in England. Unfortunately, no acceptance letter was received by him for a long time. And so, he sent a duplicate copy of the manuscript, which was entitled Plancks law and light quantum hypothesis, to Einstein in Berlin, with a request to have it translated into German and published in the Zeitschrift fur Physik. The letter in Boses own handwriting is reproduced elsewhere. Einstein immediately translated Boses paper into German and added the following note at the end : Boses derivation of Plancks formula appears to me to be an important step forward. The method used here gives also the quantum theory of an ideal gas, as I shall show elsewhere. Boses paper, translated by Einstein under the title Plancks Gesetz und Lichtquantenhypothese was published in the August 1924 issue of Zeitschrift fur Physik. After Boses paper came an avalanche of developments, the extension of Boses theory to particles of arbitrary mass and nonzero chemical potential by Einstein (1924, 1925): the FermiDirac statistics for electrons (1926), the quantization of the electromagnetic field by Heisenberg and Pauli (1929, 1930), and quantum electrodynamics by Dirac (1927, 1935). Both, Boses theory, including Einsteins extension, and Fermis theory were essentially statistical theories and dealt with complexions of the field. The actual construction of the wave functions which are symmetric and antisymmetric in the many particle systems was done by Dirac (1927). To find the relation between particle type and the statistics which is obeyed was left to Pauli (1936, 1940), who showed that integral spin particles obeyed Bose statistics and half integral spin particles obeyed Fermi statistics. In modern relativistic quantum field theory, the spinstatistics theorem involving Bosons and Fermions is one of the most fundamental results. The applicational possibilities of quantum statistics were clearly demonstrated by Sommerfeld (1928), by introducing FermiDirac statistics to metal physics. In the case of an ideal Bose gas with nonzero chemical potential, there is a critical temperature, below which a finite fraction of gas condenses into a single quantum state. This condensed phase discovered by Fritz London in 1938 should exhibit superfluid properties. London also suggested that superfluid Helium should be related to this BoseEinstein condesation phenomenon. Indeed, Boses work stands out as one of the central columns supporting the edifice of modern physics. Bose, however, did not realise the immediate impact of this paper. We may note here that the term photon for the light quantum was given by the American chemist Gilbert Newton Lewis (18751946) in 1926. The Photon GasWe had described how Max Planck (18581947) derived the black body spectral distribution in these pages earlier (Dream2047, June 2001). He considered a cavity containing the black body spectrum and postulated that all solid bodies, and therefore the walls of the cavity, contained little oscillators  or the resonators as he called them  of every imaginable frequency. By resonators Planck meant small electrified particles which wriggled to and frosurely, an assumption that is contrived and rather unaesthetic! Planck was forced to conclude that the energy levels of a material oscillator were quantised. Einstein analyzed the black body problem by considering radiation alone, and arrived at a conclusion that it was composed of quanta. He used this idea to explain the phenomenon of photoelectricity (Dream2047, May 2001). The turning point for the photon idea came in 1923 with the discovery of the Compton effect. A photon when scattered by material objects, say free electrons, loses a part of its energy with a consequent decrease in its frequency. With the discovery of the Compton effect (1923), all resistance to the photon idea evaporated. It was realized that radiation had a dual character, that is wavelike and particlelike. It was at this time when Bose entered the quantum arena and set out to derive Plancks law treating radiation as a gas consisting of photons. What Bose had essentially introduced was a new counting rule for the states of a gas of photons  or the quanta of light  that explained Plancks law of thermal radiation at one stroke. While deriving Plancks law of black body spectral distribution, what one tries to do is to derive an expression for the energy density, i.e. the radiation density in the frequency interval between and +d. Planck did this by starting with material oscillators which transferred their energy to standing waves in the cavity. In his analysis of Plancks work, Einstein supposed that radiation behaved like a gas of particles, and so he distributed the available energy E amongst these gas particles. He did not talk of gas particles; but considered photons as particles. Unlike Einstein, Bose did not regard his particles as distinguishable. Einstein did not make a big fuss about his particles being distinguishable or anything like that. In those days, nobody ever considered indistinguishable particles, and like everybody else, Einstein simply assumed (implicitly) that his particles were distinguishable. In addition, he forced agreement with experimental data at high frequencies. Bose, on the other hand, treated photons to be indistinguishable. Though not explicitly stated, the method he used for counting the number of possible arrangements of photons in different energy states implied this. Only later did people realize that he had taken a remarkable step. Further, Bose took into account the two states of polarization of the photon as well (that is, he took care of photon spin). He tacitly assumed that photon number is not conserved. Indeed, Bose himself had no idea that what he had done while deriving Plancks law was really novel (see Box). This was in the year 1924 when Quantum Mechanics had still not appeared on the scene. The photon had just been accepted. People did not know anything about spin, about Bosons and Fermions, and that they obeyed different statistics, and so on. All these developments occurred rapidly within the next few years. Many people made discoveries and every discovery influenced every other. It is against this background that we must view Boses contribution to appreciate how it merged into the mainstream to contribute to the pool of knowledge. Bose achieved two things ahead of quantum mechanics. First, he discovered indistinguishability. Indistinguishability is a natural product of quantum mechanics. But Bose sensed indistinguishability even earlier. Secondly, after people realised that quantum mechanics demands indistinguishability, it was found that there were two broad families of indistinguishable particles namely, Bosons and Fermions. After quantum mechanics came quantum statistical mechanics, which essentially deals with how quantum particles share energy at finite temperatures. By contrast, in the quantum mechanics as developed by Heisenberg and Schrodinger, there was no temperature. Hence, quantum statistical mechanics was the next step. Bose laid part of the foundation for quantum statistical mechanics even before quantum mechanics was born! We are now in a position to describe how a fixed total amount of energy is distributed among the various members of an assembly of identical particles. For a conceptual understanding and completeness, we shall briefly outline how molecules of a gas, Bosons and Fermions behave following different statistics. Figure 1:Distribution of Boltzmann ,Bose and Fermi particles , given the same choice of energy levels (Source :Bose and his statistics by G.Venkataraman) Figure 2 :Bosons and Fermions (Source :Bose and his statistics by G.Venkataraman) Molecules of a gas, Bosons and FermionsWe made a remark earlier that soon after the development of quantum mechanics, came quantum statistical mechanics, which essentially deals with how quantum particles share energy at finite temperatures. In any case statistical mechanics attempts to relate the macroscopic properties of an assembly of particles to the microscopic properties of the particles themselves. Statistical mechanics, as its name implies, is not concerned with the actual motions or interactions of individual particles, but investigates instead their most probable behaviour. While Statistical Mechanics cannot help us determine the life history of a particular particle, it is able to inform us of the likelihood that a particle (exactly which one we cannot know in advance) has a certain position and momentum at a certain instant. Because so many phenomena in the physical world involve assemblies of particles, the value of a statistical rather than deterministic approach is clear. Owing to the generality of its arguments, statistical mechanics can be applied with equal facility to classical problems (such as that of molecules in a gas) and quantummechanical problems (such as those of free electrons in a metal or photons in a box), and it is one of the most powerful tools of the theoretical physicist. We come across assemblies of three kinds of particles :
Figure 5 : FermiDirac statistics We used two new terms while describing Bosons and Fermions, viz. spin and the exclusion principle. Let us describe what both mean. Spin refers to the intrinsic angular momentum possessed by the particle (independent of any orbital angular momentum) it might have. One could crudely compare this situation with the Earth moving in its orbit around the Sun. Besides possessing orbital angular momentum as a result of its motion around the Sun, the Earth also spins about an axis passing through the poles, thereby possessing spin angular momentum. However, remember this is a very crude analogy. Quantum mechanically the situation is not so very simple. What is important is to note that while any number of photons (spin 1) could be accommodated in any available quantum energy state, it is not so with Fermions. Fermions obey a fundamental principle discovered by Wolfgang Pauli (19001958) in 1925 called the exclusion principle, according to which no two Fermions can exist in the same quantum state. For electrons, it would mean that every electron in an atom occupying a particular quantum state cannot have any other electron in the same state. So, given the same choice of energy states, how would Boltzmann particles, Bosons and Fermions fill up these energy states? Behaviour of Boson and Fermions is shown in Figure 1. The figure shows that given the same choice of energy levels, the Boltzmann particles (a), the Bose particles (b) and the Fermi particles (c) can distribute themselves. The Boltzmann particles are distinguishable, and there is no restriction about how many of them can be accommodated in an energy level. The Bosons also have a lot of freedom and can in principle all crowd into a given energy level. However, while the shuffling of Boltzmann particles can produce distinct arrangements (compare (b) and (c) where the numbers in successive levels remain the same but the occupancy is by different particles), shuffling of Bosons or Fermions does not produce anything new. Ther Fermions are very, very reserved, meaning that they do not occupy a level which is already occupied. In short, just one particle per level in strict accordance with Pauli exclusion principle. However, it is interesting to note that at high enough temperatures, both Bosons and Fermions behave like Boltzmann particles. Figure 2 brings out an important difference between Bosons and Fermions. Compare (a) and (c) which show the occupancy of the available energy levels at the lowest temperature possible, i.e. T=0 K (i.e. 273.16 0^{C}) or absolute zero. At T=0 K, the total energy of the system must be a minimum. Bosons achieve this minimum total energy by all of them crowding together into the lowest energy state. The Fermions also keep the total energy to a minimum, but they must have their single accommodation, as in (c). In the figure, (b) and (d) show what happens at nonzero absolute temperatures. The particles now spread themselves out and start occupying higher levels which they avoided at T= 0 K. However, Fermions still keep aloof from each other and have single occupancy in each state. The three distributionsLet us see how Maxwell Boltzmann, BoseEinstein and FermiDirac distributions look like. We shall not go into the details of calculations or the derivations of these distributions, but only give the expressions for them. In the formulas that follow, Ni is the number of particles which are in the state i with energy ui.gi is the number of states that have the same energy ui. The three statistical distribution laws are as follows: MaxwellBoltzmann distribution : The expression N_{i} = gi / e . e uI / kT is called the the MaxwellBoltzmann distribution followed by the molecules of a gas. Bose Einstein distribution : The expression Ni= gi / e^{} . e ^{uI / kT  1 }is called the BoseEinstein distribution. When the total number of Bosons is conserved, i.e. when the number of Bosons does not change, is nonzero. However, when we are dealing only with photons, their number is not conserved, i.e. it can change. Unlike the gas molecules or electrons, photons may be created or destroyed. would then assume the value zero. Hence the expression would reduce to Ni = gi / e uI / kT1. While deriving Plancks law, the total radiant energy within the cavity must remain constant, however, the number of photons that incorporate this energy can change. This equation immediately leads to Plancks radiation formula once gi is calculated following Boses prescription of filling up the quantum states. Figure 6: BoseEinstein condensate observed experimentally. Falsecolor images display the velocity distribution of the cloud of rubidium atoms at just before the appearance of the BoseEinstein condensate, just after the appearance of the condensate, and after further evaporation left a sample of nearly pure condensate. The field of view of each frame is 200x270 micrometers, and corresponds to the distance the atoms have moved in about 1/20 of a second. The colour corresponds to the number of atoms at each velocity, with red being the fewest and white being the most. Areas appearing white and light blue indicate lower velocities. Fermi Dirac distribution : The expression N_{i} = g_{i} / e . euI / kT+1 is called the Fermi Dirac distribution and incorporates the Pauli exclusion principle explained earlier. The quantity f(ui) = ni /gi is called the occupation index of a state of energy ui, and is the average number of particles in each of the states of that energy. The occupation index does not depend upon how the energy levels of a system of particles are distributed, and for this reason it provides a convenient way of comparing the essential natures of the three distribution laws. The MaxwellBoltzmann occupation index is plotted in Fig. 3 for three different values of T and . This Index is a pure exponential, dropping by the factor 1/e for each increase in ui of kT. The BoseEinstein occupation index is plotted in Fig. 4 for temperatures of 1000 K, 5000 K, and 10,000 K, in each case for = 0 (corresponding to a gas of photons). When u_{i}< >_{ > > kT, the BoseEinstein distribution approaches the MaxwellBoltzmann distribution, while when ui <> }
Wolfgang Ketterle
BoseEinstein CondensationIt was Einstein who had an additional deep insight into the consequences of Boses counting rule. In view of the fact that helium atoms have spin zero, they also would behave like a Boson gas. BoseEinstein statistics can then be applied to study their behaviour. In the case of photons, the total number of particles actually decreases as we decrease the total energy of the system (equivalently, as we lower the temperature). However, if we apply Bose statistics to a gas of helium atoms in a box, we must obviously keep the number of atoms fixed as the temperature varies. So the precise formula for the number of atoms in a state with energy ui is different from what Bose used in the case of photons as we have described earlier, though it looks very similar. It contains an additional term as stated in the expression for the BoseEinstein particles. This has the effect of subtracting a term from ui. But, it has profound consequences. As the temperature is lowered, more and more particles pile into the lowest energy stated. (For the gas of photons, they just disappear from the system). At a low temperature, but one which is still above absolute zero, the answer for the number of particles in the lowest state becomes infinite. Here, we have Bosons behaving like birds that flock together! Einstein realized that this infinite answer, though wrong, held the key to what was really happening in the gas as it was being cooled. He boldly said that one has to treat the lowest energy state as a separate entity from all the other states. All physical quantities would receive separate contributions from the lowest state, called the condensate, and from all other states. In a Bolzmann gas the contribution of any single state, even the one of lowest energy, is negligible because there are so many states which have nearby energies. But the Bose counting rule tilts the balance in favour of a finite fraction of the particles being in the lowest energy state, below the special value of the temperature which Einstein had calculated. Surely he had a deep conviction that Boses counting rule was not just a trick to understand radiation but a new general principle. When liquid helium is supercooled to temperatures below 2.1 K, it starts behaving in a strange manner. Its viscosity suddenly decreases, its heat conductivity is abnormally large. It behaves like a superfluid. In 1938, eminent quantum and statistical physicist Fritz London (19001954) suggested that the new properties exhibited by liquid helium were a consequence of BoseEinstein condensation. Recent experiments, sixty years after London, show that his guess regarding liquid helium was right. This subject took another turn in 1995, when experimenters in the USA were able to produce a Bose Einstein condensate for rubidium atoms. Got it at last !To achieve BoseEinstein condensation, a gas must be cooled to less that one millonth of a degree above absolute zero. The 1997 Nobel prize winners (Steven Chu, Claude Cohen Tannoudji and William Phillips) had developed effective laserbased methods for cooling and trapping atomic gases, but the path to BoseEinstein condensation remained extremely difficult. Carl Wieman (JILA and University of Colorado, Boulder, U.S.A.), pointed toward a successful method: laser cooling of alkali atoms in a socalled magnetooptical atom trap and then continued reduction of speed through evaporative cooling, which is a way of systematically getting rid of the fastest atoms. After extensive efforts by the research team in Colorado, Eric Cornell (at JILA and National Institute of Standards & Technology, Boulder, U.S.A.) solved the last remaining problem that prevented condensation. Cornell and Wieman produced a pure condensate of about 2000 rubidium atoms at an unbelievably low temperature of 20 nanoKelvin, i.e. 0.000 000 02 degrees above absolute zero. The successful experiments using rubidium atoms were reported in 1995 (Figures 6). Wolfgang Ketterle (Massachusetts Institute of Technology, U.S.A.) worked independently of Cornell and Wieman, and four months after them he reported large condensates of lasercooled sodium atoms. Ketterle was able to demonstrate that the condensate actually behaved as a single coherent wave. He did an experiment similar to the one where two stones are thrown simultaneously at a calm water surface and their wave patterns roll into each other, strengthening and weakening each other in a systematic way. This is in greater contrast to what happens when uncoordinated matter, for example two fistfuls of sand, are thrown on the water surface. Ketterle was also able to extract a beam of coherent matter from the condensate, thus achieving the firstatom laser. An ordinary laser yields coherent radiation, an atom laser a stream of coherent matter. When a gas consisting of uncoordinated atoms turns into a BoseEinstein condensate, it is like when the various instruments of an orchestra with their different tones and timbres, after warming up individually, all join in the same tone. Here we have Bosons not only behaving like birds that flock together, but also sing together! After the pioneering experiments of 2001 Laureates, condensates have now been achieved by more than twenty additional research teams. Many fascinating applications are conceivable. Precision measurements utilizing slow atoms may offer big surprises: perhaps what we today call natural constants are completely constant. The new control over matter the BoseEinstein condensation provides may have farreaching practical applications, for example in lithography and nanotechnology.
References 1. Satyendra Nath Bose 2.Concepts of Modern Physics 3. Bose and his Statistics By G. Venkataraman Sangam Books Limited By arrangement with Universities Press (India) Ltd., 1992 Hyderabad A delightful book written in popular style with a number of anecdotes and related information. This article partly draws on it. 4. A Treatise on Heat 5. S.N. Bose : The Man and his work 6. http://www.nobel.se 7. http://physicsweb.org/article/world/10/3/3 Bose Einstein
Condensation (Feature March 1997) 8. The Story of Photon 9. Bose Einstein Condensation 10. Bose Einstein Condensation revisited 11. http://jilawww.colorado.edu
BosonsThe birds that flock and sing together : GlossaryImportant terms used in connection with BoseEinstein Statistics are given below. The terms given do not necessarily appear in the present article.
Angular momentum : The cross product of a vector from a specified reference point to a particle, with the particles linear momentum. Also known as moment of momentum. BardeenCooperSchrieffer theory : A theory of superconductivity that describes quantummechanically those states of the system in which conduction electrons cooperate in their motion so as to reduce the total energy appreciably below that of other states by exploiting their effective mutual attraction; these states predominate in a superconducting material. Abbreviated BCS theory. BoseEinstein condensation : A phenomenon that occurs in the study of systems of bosons; there is a critical temperature below which the ground state is highly populated. Also known as condensation; Einstein condensation. BoseEinstein distribution : For an assembly of independent bosons, such as photons or helium atoms of mass number 4, a function that specifies the number of particles in each of the allowed energy states. Also known as Bose distribution. BoseEinstein statistics : The statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may exist in the same state simultaneously. Also known as EinsteinBose distribution. Bose gas : An assemblage of noninteracting or weakly interaction bosons. Boson : A particle that obeys BoseEinstein statistics; includes photons, pi mesons, and all nuclei having an even number of particles and all particles with integer spin. Cooper pairs : Pairs of bound electrons which occur in a superconducting medium according to the BardeenCooperSchrieffer theory. Exclusion principle : The principle that no two Fermions of the same kind may simultaneously occupy the same quantum state. Also known as Pauli exclusion principle. Laser : A device that uses the principle of amplification of electromagnetic waves by stimulated emission of radiation. Derived from light amplification by stimulated emission of radiation. Liquid helium : The state of helium which exists at atmospheric pressure at temperatures below 268.95C (4.2K), and for temperatures near absolute zero at pressures up to about 25 atmospheres; has two phases, helium I and helium II. MaxwellBoltzmann distribution : A function giving the probability (or some function proportional to it) that a molecule of a gas in thermal equilibrium will have values of certain variables within given infinitesimal ranges, assuming that the gas molecules obey classical mechanics, and possibly making other assumptions. MaxwellBoltzmann statistics : The classical statistics of identical particles, as opposed to the BoseEinstein or FermiDirac statistics. Also known as Boltzmann statistics. Phase space : For a system with n degrees of freedom, a Euclidean space with 2n dimensions, one dimension for each of the generalized coordinates and one for each of the corresponding momenta. Photon : A massless particle, the quantum of the electromagnetic field, carrying energy, momentum, and angular momentum with spin angular momentum 1. Also known as light quantum. Photon gas : An electromagnetic field treated as a collection of photons; it behaves as any other collection of bosons, except that the particles are emitted or absorbed without restriction on their number. Photon theory : A theory of photoemission developed by Einstein, according to which a light beam behaves like a stream of particles (called photons) when it delivers energy to a substance displaying photoemission, the particles each having an energy equal to Plancks constant times the frequency of the light. Planck oscillator : An oscillator which can absorb or emit energy only in amounts which are integral multiples of Plancks constant times the frequency of the oscillator. Also known as radiation oscillator. Planck radiation formula : A formula for the intensity of radiation emitted by a blackbody within a narrow band of frequencies (or wavelengths), as a function of frequency, and of the bodys temperature. Also known as Planck distribution law; Plancks law. Plancks constant : A fundamental physical constant, the elementary quantum of action; the ratio of the energy of a photon to its frequency, it is equal to 6.62620 + 0.00005 X 1034 joulesecond. Symbolized h. Plancks law : A fundamental law of quantum theory stating that energy associated with electromagnetic radiation is emitted or absorbed in discrete amounts which are proportional to the frequency of radiation. Statistical mechanics : That branch of physics which endeavors to explain and predict the macroscopic properties and behaviour of a system on the basis of the known characteristics and interactions of the microscopic constituents of the system, usually when the number of such constituents is very large. Also known as statistical thermodynamics. Statistics : A discipline dealing with methods of obtaining data, analyzing and suymmarizing it, and drawing inferences from data samples by the use of probablility theory. Steady state : The condition of a body or system in which the conditions at each point do not change with time, that is after initial transients or fluctuations have disappeared. Superconductivity : A property of many metals, alloys, and chemical compounds at temperatures near absolute zero by virtue of which their electrical resistivity vanishes and they become strongly diamagnetic. Superconductor : Any material capable of exhibiting superconductivity; examples include iridium, lead, mercury, niobium, tin, tantalum, vanadium, and many alloys. Also known as cryogenic conductor; superconducting material. Superfluid : A collection of particles which obey BoseEinstein statistics and are all in the lowest energy state allowed by quantum mechanics, having zero entropy and zero resistance to motion; examples are a fraction of the atoms in liquid helium II and a fraction of the pairs of electrons in a superconductor. Superfluidity : The frictionless flow of liquid helium at temperatures very close to absolute zero through holes as small as 107 centimeter in diameter, and for particle velocities below a few centimeters per second. 
Top Science Discoveries in 2001Year 2001 has gone by .But it was witness to a number of important happenings in science and technology. Year 2001 was the 100th anniversary of the Nobel prizes. A lot of discoveries and inventions have taken place in this year. Below is a quick review of important stories, some are because of their significance and others just because they are fun. SpintronicsNearly every electrical and electronics gadget is based on electrons property, in which negative charge plays a very important role. But apart from charge, electrons possess another fundamental trait namely spin  that could give rise to whole new class of electronic devices. During last year, scientists made several advances in the fieldfinding way to create spin polarized electric current in semiconductors, pass electron spin from one semiconductor to another, and spin electrons using electricity. Stopping light in its tracksIn January, two independent teams of scientists announced that they had found a way to reduce the speed of light to zero. Although light in a vacuum moves at a neckbreaking 186,000 miles per second, materials with a high refractive index can slow it down. This has ample uses, in quantum computers. Worlds Most Accurate ClockSince 1967 scientists have defined a single second according to microwave frequency transitions in Cesium, ticks that occur roughly once each nanosecond. Optical transitions in atom take place more frequently and can meter out smaller divisions of time. But until recently, researchers had no way to the faster ticks. In July 2001 physicists devised the first ever allatomic clock, allowing them to divide time down to the femtosecond. Human CloningOn October 13, 2001 scientists at Advanced Cell Technology came into their laboratory to see under the microscope what they had been striving for months little balls of dividing cells not even visible to the nacked eye. As they appeared, the specks were precious because they were, according to ACT, the first human embryos produced using the technique of nuclear transplantation, popularly otherwise known as cloning. Human Genome AnalysisThe world celebrated when scientists from the Human Genome Project, an international consortium of academic research centre, and Celera Genomics, a private U.S. company, both announced that they had finished working drafts of the human genome in 2000. But these drafts revealed only the beginning of the story. In February 2001 both teams announced the results of their initial analysis which revealed among other surprises, that humans have a mere 26,000 to 40,000 genes or far fewer than people predicted. Complied by : Kapil Tripathi
