The effect of quenched impurities on systems undergoing first-order phase transitions is studied within the framework of the $q$-state Potts model. For large $q$ a mapping to the random-field Ising model explains the absence of any latent heat in 2D, and suggests that for $d>\mathrm{}2\mathrm{}$ such systems exhibit a tricritical point with an exponent $\nu$ related to those of the random-field model by $\nu ={\nu }_{\mathrm{RF}}/(2-{\alpha }_{\mathrm{RF}}-{\beta }_{\mathrm{RF}})$. In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a ratio $\beta /\nu$ which varies continuously with $q$, and a weakly varying exponent $\nu \approx 1$. We find strong evidence for the multiscaling of the correlation functions.

The dynamics of self-similar free fractals is described in terms of a local energy and an effective metric, which produce intrinsic field equations and diffusion within the structure. When focused in the Lagrangian metric, basic dynamical laws exhibit natural universal scaling.

We study the classical thermodynamics of a $(1+1)$-dimensional double-well sinh-Gordon theory. Remarkably, the Schrödinger-like equation resulting from the transfer integral method is quasi-exactly solvable at several temperatures. This allows exact calculation of the partition function and some correlation functions above and below the short-range order (“kink”) transition, in striking agreement with high resolution Langevin simulations. Interesting connections with the Landau-Ginzburg and double sine-Gordon models are also established.

With supersymmetric quantum mechanics, a coupled-channel potential is determined which is phase equivalent to a given one, and whose bound spectrum is identical except for one arbitrary bound state which is removed. The bound state is suppressed by a first supersymmetric transformation and the original scattering matrix is recovered with a second transformation. The resulting potential presents an $r^{-2\mathrm{}}$ singularity at the origin in some channels. The method is applied to the removal of the nonphysical state of the deep ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ neutron-proton Moscow potential and transforms it into a shallow potential with a repulsive core.

Given a set of points drawn from an unknown continuous probability distribution, one often wishes to infer the underlying distribution. This distribution can be estimated using a simple scalar field theory. Fluctuations around the estimate are characterized by a robust measure of goodness of fit, analogous to the conventional ${\chi }^2$, whose distribution can also be calculated. The resulting method of data analysis has some advantages over conventional approaches.

We determine the critical temperature of a 3D homogeneous system of hard-sphere bosons by path-integral Monte Carlo simulations and finite-size scaling. In the low density limit, we find that the critical temperature is increased by the repulsive interactions, as $\Delta T_C{/T}_0\sim ({\mathrm{na}}^3{)}^{\gamma }$, where $\gamma =0.34\mathrm{}\pm 0.03$. At high densities the result for liquid helium, namely, a lower critical temperature than in the noninteracting case, is recovered. We give a microscopic explanation for the observed behavior.

We present an analytical method to calculate the depletion of a Bose-Einstein condensate excited in a time dependent harmonic trap. We identify a regime where the motion of the condensate is unstable and show that this instability leads to an exponentially fast population of noncondensed modes. As these modes are concentrated on the surface of the condensate this is observable in the particle density.

We develop a reliable procedure for calculating the microcanonical fluctuations of the ground state occupation number for harmonically trapped ideal Bose gases, and show that these fluctuations vanish uniformly when the temperature approaches zero. The key point is the precise determination of the number of microstates from the canonical partition sum, thus avoiding a failure of the usual saddle point method. We also demonstrate why the magnitude of the condensate fluctuations does not depend on the total particle number.

The simplest model for studying N-body gravitational interactions is the one-dimensional system consisting of parallel mass sheets [one-dimensional self-gravitating system (OGS)]. The model has been used often to test theories of gravitational evolution. Here we demonstrate that a two mass-component OGS with initial conditions selected far from equilibrium attains both mass segregation and equipartition of energy in a long, but finite, time. This may be the first clear evidence of the approach to thermal equilibrium in this type of system. The implications of these findings as well as future investigations are discussed.

The problem of the statistical description of the first passage time $t_{j,N}$ to a given distance $r$ of the first $j$ of a set of $N$ noninteracting diffusing particles, all starting from the same origin on fractal substrates, is addressed. Asymptotic expressions (the main and two corrective terms) for large $N$ of the (arbitrary) moments of $t_{j,N}$ are given. It is shown that, to first order and for $1\le j\ll N$, the $m$th moment of $t_{j,N}$ goes as $(\ln N{)}^{m\left({1-d}_w\right)}$, and its variance as $(\ln N{)}^{{-2d}_w}$, $d_w$ being the anomalous diffusion exponent of the fractal medium.

We show that attractive interactions between molecules adsorbed in molecular sieves play a vital role in the mechanisms and rates of intracrystalline diffusion. Over a wide temperature range, the single-file diffusion of ${\mathrm{CF}}_4$, ${\mathrm{SF}}_6$, and ${\mathrm{CCl}}_4$ in ${\mathrm{AlPO}}_4$- $5$ is dominated by the diffusion of molecular clusters. ${\mathrm{SF}}_6$ and ${\mathrm{CCl}}_4$ clusters diffuse by concerted mechanisms involving all of the cluster's molecules simultaneously. The activation energies, $E_a$, for these mechanisms are strongly size dependent and are lower than $E_a$ for monomer diffusion.

We show that a quantum system may be associated to a backward stochastic process in complex configuration space when the so-called weak value of the position operator is interpreted as a conditional expectation value. The ensemble averaged values of such a stochastic trajectory and the corresponding weak values of a quantum particle are shown to be equivalent. Moreover, the stochastic trajectory is shown to reduce to the correct classical trajectory in the limit where the de Broglie wavelength vanishes.

We determine the semiclassical coherent-state propagator for a particle going through one-dimensional evolution in a simple barrier potential. The described semiclassical method makes use of complex trajectories which, by its turn, enables the definition of (real) traversal times in the complexified phase space. We then discuss the behavior of this time for a wave packet whose average energy is below the barrier height.

Tailored complex potentials for atoms can be made of two overlapping standing light waves, one on resonance and one far detuned. The observed diffraction asymmetry of Bragg diffraction of such light structures is due to a corresponding asymmetry of the Fourier components of the potential. In crystal physics this is known as a violation of Friedel's law.

We consider the self-evolution of strongly nonequilibrium interacting Bose gas. Because of the mere fact of large (relative to unity) occupation numbers in the initial state the problem is directly reduced to the question of temporal evolution of the statistical matrix diagonal in the coherent-state representation. Strictly speaking, gauge symmetry is not destroyed even when the long-range ordering is completed, owing to the inevitable averaging over the ensemble. Actual symmetry breaking can occur only as a result of introducing a small term of the Hamiltonian violating conservation of particles, or quantum-mechanical measurement, also implying nonconservation of particles.

We study Brownian motion in chains of segments with flashing sawtoothlike potentials. In all former models for stochastic ratchets a coherent switching of the potential is assumed. We consider the generalized case which allows independent switchings of the potential in single segments. We introduce three different rules: correlated, anticorrelated, and uncorrelated switchings. On the basis of a discrete model analytical results for the mean flux are compared with computer simulations. As a result the mean flux will be enhanced for anticorrelated and uncorrelated sawteeth as compared with the case of correlated (coherent) segments.

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. Analytic results for the stationary state are presented in mean-field approximation, exhibiting a novel type of first order phase transition related to dynamic freezing. Monte Carlo simulations performed on a quadratic lattice indicate that many features of the mean-field theory may survive the presence of fluctuations.

It is proven experimentally that the ortho-para conversion of the nuclear spin isomers of ${}^{13}{\mathrm{CH}}_3\mathrm{F}$ molecules can be slowed down by increasing the gas pressure. The observed “freezing” of the molecular quantum states can be considered as an example of the quantum Zeno effect induced by collisions.

A Lindblad operator is proposed to describe quantum dynamics of an open system with linear dissipation. Its functional form is determined based on the microscopic Caldeira-Leggett model. It yields a new master equation which preserves positive density evolution on short times and approaches equilibrium at high and low temperatures. The new master equation is applied as an example to study the femtosecond dynamics of vibrational relaxation and desorption at a metal surface.

We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of condensate stability. It plays the same role as the sign of scattering length in a one-species condensate. We predict that there is a range of interspecies interaction strength in which a sodium-rubidium mixture can be stable in a harmonic trap.