A new method to treat statistical mechanics in a polydisperse system is described, applicable when the nonideal part of the free energy depends only on a few moments of a size distribution. A simple entropic contribution to the free energy is identified from combinatorial considerations. Although approximate in the general case, the method obtains the exact spinodal curve, critical points, cloud curve, and shadow curve. Polydisperse Flory-Huggins theory is treated as an example.

Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the “hypothesis of equal weights for eigenstates,” we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.

We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity $D_c$, or equivalently a critical temperature $T_c$, at which the mean velocity of particles is zero. Below $T_c$ and above $T_c$ particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.

We study nonlinear behavior in a model of a periodically modulated, overdamped rf SQUID loop operating in the dispersive (i.e., nonhysteretic) mode. In the presence of correlated noise we find an enhancement of the output signal-to-noise ratio (SNR) as a function of the nonlinearity parameter of the device. The calculation involves knowledge only of the input-output transfer characteristic of the device. These signal enhancement properties appear to be generic to devices characterized by nonlinear transfer characteristics. We also use our transfer characteristic approach to explain recent experimental results showing SNR enhancement in dc SQUIDs as a function of dc bias current and flux.

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits and treat the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. We test the model and find agreement between our predictions and empirical results based on a large economics database spanning 20 years.

We report on a quantum optical experimental implementation of teleportation of unknown pure quantum states. This realizes all of the nonlocal aspects of the original scheme proposed by Bennett et al. and is equivalent to it up to a local operation. We exhibit results for the teleportation of a linearly polarized state and of an elliptically polarized state. We show that the experimental results cannot be explained in terms of a classical channel alone. The Bell measurement in our experiment can distinguish between all four Bell states simultaneously allowing, in the ideal case, a 100% success rate of teleportation.

The noisy Burgers equation in one dimension is treated by a nonlinear soliton approach based on the Martin-Siggia-Rose technique. In a canonical formulation the strong coupling fixed point is accessed by a principle of least action in the asymptotic nonperturbative weak noise limit. The scaling behavior and the growth morphology are described by a gas of solitons and a superposed gas of linear modes. The gapless soliton dispersion yields the dynamic exponent. The roughness exponent and the scaling function, of the form of a Lévy distribution, follow from a spectral representation of the interface slope correlations.

We present theoretical studies of a two-species Bose condensate. Using a new numerical method, we have calculated ground state wave functions and show that, due to interspecies interactions, the condensate mixture displays novel behavior not found in a pure condensate. We compared our results with those of the Thomas-Fermi approximation (TFA) and find that under a broad range of conditions the TFA can be reliably used to predict many qualitative features of the condensates. Using our technique, we have modeled a recent JILA experiment on dual spin-state ${}^{87}\mathrm{Rb}$ condensate. Finally, collective excitations of double condensates are discussed.

We present a new theoretical treatment of the collective excitation spectrum of a two-species Bose-Einstein condensate confined in a magnetic trap. We show that the interspecies interaction significantly modifies the excitation spectrum and gives rise to a rich set of new phenomena. We identify a novel metastable state of the double condensate and show that under external perturbation there can be a macroscopic quantum transition between this metastable state and the true ground state of the double condensate system.

A Comment on the Letter by Dipankar Home and Rajagopal Chattopadhyay, Phys. Rev. Lett. 76, 2836 (1996). The authors of the Letter offer a Reply.

A Reply to the Comment by Philip Pearle and Euan Squires.

We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical finite-temperature Green functions. Specifically, the orbital magnetism is greatly enhanced by the combined effects of interactions and finite size. The presence of families of periodic orbits in regular systems makes their susceptibility parametrically larger than that of chaotic systems, a difference which emerges from correlation terms.

We have devised a way to trap atoms above a magnetic surface using the Zeeman effect. The method is generally applicable to any paramagnetic atom with hyperfine structure and results in very strong confinement and, hence, a high vibrational frequency perpendicular to the surface. This allows the atomic de Broglie wave to propagate as in a single-mode 2D waveguide. We show how atoms can be continuously and unidirectionally coupled with high efficiency into the lowest mode of the waveguide. This invention makes possible the study of weakly interacting gases in 2D.

Treating a many-body Fermi system in terms of a single particle in a deforming mean field, we relate adiabatic geometric phase to susceptibility for the noncyclic case, and to its derivative for the cyclic case. Employing the semiclassical expression of the susceptibility, the expression for geometric phase for chaotic quantum system immediately follows. Exploiting the well-known association of the absorptive part of susceptibility with dissipation, our relations may provide a quantum mechanical origin of the damping of collective excitations in Fermi systems.

Quantum teleportation is analyzed for states of dynamical variables with continuous spectra, in contrast to previous work with discrete (spin) variables. The entanglement fidelity of the scheme is computed, including the roles of finite quantum correlation and nonideal detection efficiency. A protocol is presented for teleporting the wave function of a single mode of the electromagnetic field with high fidelity using squeezed-state entanglement and current experimental capability.

A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest-neighbor exchanges that conserve each of the three species. For the case in which the three densities are equal, it is shown that the model obeys detailed balance. The Hamiltonian governing the steady state distribution in this case is given and is found to have long range asymmetric interactions. The partition sum and bounds on some correlation functions are calculated analytically demonstrating phase separation.

By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing N sites and p particles. Using this expression we easily recover the exact diffusion constant obtained earlier and calculate as well some higher cumulants. The distribution of the deviation y of the average current is, in the limit $N\to \infty$, skew and decays like $\exp -\left({\mathrm{Ay}}^{5/2}\right)$ for $y\to +\infty$ and $\exp -\left(A^{\prime }|y{|}^{3/2}\right)$ for $y\to -\infty$. Surprisingly, the large deviation function has an expression very similar to the pressure (as a function of the density) of an ideal Bose or Fermi gas in 3D.

We propose a new class of differential equations, which we call local fractional differential equations. They involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time. A local fractional analog of the Fokker-Planck equation has been derived starting from the Chapman-Kolmogorov condition. We solve the equation with a specific choice of the transition probability and show how subdiffusive behavior can arise.

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The formalisms developed here are expected to be useful in the discussion of nonextensive systems.