Recovering information borne by quanta that crossed the black hole event horizon

In this essay we discuss how the statistics of quantum particles, namely, stimulated emission for bosons and the exclusion principle for fermions, provide mechanisms for correlating the radiations impinging and emanating from a black hole. In either case, the information originally borne by the incoming radiation that is partially transferred to the outging radiation is estimated within the framework of communication theory.     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

Classical and quantum statistics as finite random processes

We show: (1) It is possible to produce the three familiar statistics without referring to the problem of distinguishability; (2) what really distinguishes elementary particles is the correlation existing among them; (3) correlations existing among quantum particles, positive for bosons and negative form fermions, are completely different in character.     

Quantum liquids of particles with generalized statistics

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low-temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide an explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and f-sum rules.     

Role of quantum statistics in multi-particle decay dynamics

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.     

Quantum theory for a special kind of hard-core particles with intermediate statistics

Starting from a specific definition of fractional statistics for hard-core particles, we find a set of intermediate statistics systems, in which a single-particle quantum state can be effectively occupied by an integer number of identical particles — M-ons, as in the case for fermions and bosons. A quantum statistical theory of an ideal M-on gas is formulated exactly, and the associated distribution is explicitly represented in a simple analytical form. A possible application to the fractional quantum Hall effect is also briefly discussed.     

Capacities of quantum channels for massive bosons and fermions

We consider the capacity of classical information transfer for noiseless quantum channels carrying a finite average number of massive bosons and fermions. The maximum capacity is attained by transferring the Fock states generated from the grand-canonical ensemble. Interestingly, the channel capacity for a Bose gas indicates the onset of Bose-Einstein condensation, by changing its qualitative behavior at the criticality, while for a channel carrying weakly attractive fermions, it exhibits the signatures of Bardeen-Cooper-Schrieffer transition. We also show that, for noninteracting particles, fermions are better carriers of information than bosons.     

n-Particle Quantum Statistics on Graphs

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.     

A unified grand canonical description of the nonextensive thermostatistics of the quantum gases: Fractal and fractional approach

In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered. Received 17 September 1999     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Atomic Bose-Fermi mixtures in an optical lattice

A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.     

Universal vortex formation in rotating traps with bosons and fermions

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.     

Quantum monte carlo algorithm based on two-body density functional theory for fermionic many-body systems: application to 3He

We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was used.     

Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems,by Maciej Lewenstein,Anna Sanpera and Verònica Ahufinger

A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.     

The Pauli Exclusion Principle. Can It Be Proved?

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory.     

One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.     

THE COMPOSITE MODEL OF LEPTON AND QUARK WITH ONLY ONE CONSTITUENT SCALAR

We propose a composite model of leptons and quarks containing two constituent fermions of spin 1/2 and a constituent scalar. The constituent fermions are massless and color singlets. Leptons, quarks and weak vector bosons are composites confined by SU(3)_H local gauge interaction, where leptons are made of three constituent fermions and quarks are two-body composites of a scalar and a fermion. The number of the constituent particles is less in our model. There are less exotic leptons and quarks. Quark-lepton parallelism holds. Weak interactions appear only at the composite level as residual short-range interactions among hypercolor singlets. The violation of parity occurs by the mechanism of dynamical symmetry breaking.     

Search for elementary quantum statistics

Bose-Einstein and Fermi-Dirac are the main quantum statistics. Therefore, it is likely that if truly elementary building blocks of Nature exist, they are either bosons or fermions, so that it is also likely that one, and only one, of the following possibilities, concerning those elementary building blocks, is correct: (i) all of them are fermions; (ii) some of them are bosons, others fermions; (iii) all of them are bosons; (iv) the distinction between these cases is methodological, not physical. Since tensors can be constructed from spinors, most physicists support one of the first two points of view. However, by starting from the fact that now it is known that bosonization makes sense, and developing a former research by Penney, we defend the point of view that, at least in a finite model of the Universe, the third point of view is the more likely. To avoid confusion we state that we are not concerned with the whole set of the so-called “elementary particles” since most physicists believe by now that, e.g., hadrons are built from quarks, nor concerned with quarks since many physicists suspect they are also composite objects. This research concerns the true elementary building blocks of Nature, assuming that such set exists, whatever those building blocks are. Finally, we extend this research to general finite associative algebras, enlarging the physical applicability of our point of view concerning the role of bosons in Nature.