The static response of a canonical quantum ensemble to linear changes in its Hamiltonian is the basis for the formulation of a phase space with classical-like properties. Classical-like time-dependent correlation functions provide an exact representation of Kubo quantum correlation functions. The formulation of this phase space allows for (i) a deep understanding of dynamical approximations previously derived within the path integral formulation of statistical mechanics and (ii) improved dynamical approaches.

The quon algebra describes particles, “quons,” that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons ( $q=+1\mathrm{}$) and fermions ( $q=-1\mathrm{}$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that $q_{\mathrm{composite}}{=q}_{\mathrm{constituent}}^{n^2}$ for a system of $n$ identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.

Bohr's correspondence principle, i.e., the expectation that the semiclassical approximation works better for states with greater quantum numbers, is shown to break down in all quantum systems in which the asymptotic interaction between the fragments behaves as ${-C}_n/r^n$ with $n>\mathrm{}2\mathrm{}$.

A neutral, ground-state, ${}^4\mathrm{He}$ atom beam has been focused using Fresnel zone plates. At only moderate demagnification $(0.40\times )$, a focused spot diameter of $\le 2.0\mu \mathrm{m}$ is achieved at a signal intensity of 500 counts/s. This is an improvement over previous work by a factor of 10 in resolution, ${10}^3$ in signal intensity, and ${10}^8$ in focused beam density, and allows the full intrinsic intensity profile of a focused atomic Fresnel spot to be measured for the first time. Raster scans of 15 and $25\mu \mathrm{m}$ wide slits across the focused spot demonstrate transmission scanning helium de Broglie microscopy of micron resolution.

We study the one-dimensional Ising model with long-range interactions in the context of Tsallis nonextensive statistics by computing numerically the number of states with a given energy. We find that the internal energy, magnetization, entropy, and free energy follow nontrivial scaling laws with the number of constituents $N$ and temperature $T$. Each of the scaling functions for the internal energy, the magnetization, and the free energy, adopts three different forms corresponding to $q>\mathrm{}1\mathrm{}$, $q=1\mathrm{}$, and $q<\mathrm{}1\mathrm{}$, $q$ being the nonextensivity parameter of Tsallis statistics.

We suggest an experiment to investigate interference effects between two spatially separated Bose-Einstein condensates. In the presence of coherence, the dynamic structure factor, measurable through inelastic photon scattering, is predicted to exhibit, at high momentum transfer $q$, interference fringes with frequency period $\Delta \nu =q/\mathrm{md}$, where $d$ is the distance between the condensates. We show that this coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates can be, hence, created through the measurement process.

We present a method, for highly efficient free-energy calculations by means of molecular dynamics and Monte Carlo simulations, which is an optimized combination of coupling parameter and adiabatic switching formalisms. This approach involves dynamical reversible scaling of the potential energy function of a system of interest, and allows accurate determination of its free energy over a wide temperature interval from a single simulation. The method is demonstrated in two applications: crystalline Si at zero pressure and a fcc nearest-neighbor antiferromagnetic Ising model.

Atomic two-photon $J=0\mathrm{}\leftrightarrow J^{\prime }=1\mathrm{}$ transitions are forbidden for photons of the same energy. This selection rule is related to the fact that photons obey Bose-Einstein statistics. We have searched for small violations of this selection rule by studying transitions in atomic Ba. We set a limit on the probability $v$ that photons are in exchange-antisymmetric states: $v<\mathrm{}1.2\mathrm{}\times {10}^{-7\mathrm{}}$.

All bell- and kink-shaped solitons sustained by an infinite periodic atomic chain of arbitrary anharmonicity are worked out by solving a second-order, nonlinear differential equation involving advanced and retarded terms. The asymptotic time decay behaves exponentially or as a power law according to whether the potential has a harmonic limit or not. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Lattice and continuum solitons differ markedly from one another.

A model, consisting of triangular trimers on the triangular lattice is presented. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated by rigid domain walls. The transfer matrix can be diagonalized by a Bethe Ansatz with two types of particles. This leads to an exact expression for the entropy on a two-dimensional subset of the parameter space.

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in $S^2$, can be colored so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-overclassical advantage for information processing can be derived from the Kochen-Specker theorem alone.

Meyer [Phys. Rev. Lett. 83, 3751 (1999)] recently showed that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can be effectively nullified if only finite precision measurements are considered. We generalize this result: one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker-like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over all possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

We show that the conductance of atoms through a tightly confining waveguide constriction is quantized in units of ${\lambda }_{\mathrm{dB}}^2/\pi$, where ${\lambda }_{\mathrm{dB}}$ is the de Broglie wavelength of the incident atoms. Such a constriction forms the atom analog of an electron quantum point contact and is an example of quantum transport of neutral atoms in an aperiodic system. We present a practical constriction geometry that can be realized using a microfabricated magnetic waveguide, and discuss how a pair of such constrictions can be used to study the quantum statistics of weakly interacting gases in small traps.

We consider the effect of the indirect interaction due to the exchange of density fluctuations on the critical temperature of superfluid ${}^6\mathrm{Li}$. We obtain the strong coupling equation giving this critical temperature. This equation is solved approximately by retaining the same set of diagrams as in the paramagnon model. We show that, near the instability threshold, the attractive interaction due to density fluctuations gives rise to a strong increase in the critical temperature, providing a clear signature of the existence of fluctuation induced interactions.

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase $K_0({\mathrm{na}}^3{)}^{1/6}$, where $n$ is the density, $a$ is the $S$-wave scattering length, and $K_0$ is a constant given in the paper. This disagrees with all existing results, analytical or numerical.

We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and, hence, is nonuniversal.

We examine two simple and feasible practical schemes allowing the complete determination of any quantum measuring arrangement. This is illustrated with the example of parity measurement.

We investigate the evolution of Bose-Einstein condensates falling under gravity and bouncing off a mirror formed by a far-detuned sheet of light. After reflection, the atomic density profile develops splitting and interference structures which depend on the drop height, on the strength of the light sheet, as well as on the initial mean field energy and size of the condensate. We compare experimental results with simulations of the Gross-Pitaevski equation. A comparison with the behavior of bouncing thermal clouds allows us to identify quantum features specific for condensates.

We derive a new description of two complementary classes of scalar, vector, or tensor sources, namely, nonradiating (NR) sources and sources that lack a NR part, i.e., “purely radiating” sources. The class of purely radiating sources is shown to be exactly the class of solutions—within the source's support—of the homogeneous form of the associated partial differential equation relating the sources to their fields; i.e., purely radiating sources are themselves fields. We show that this result is related to the well-known reciprocity principle and establish a new definition of a localized NR source based on that principle. A broad class of physically relevant sources, all of which possess a NR part, is identified. The role of NR sources in absorption of radiation and energy storage is addressed.