Rigorous analysis of singularities and absence of analytic continuation at first-order phase-transition points in lattice-spin models

We report about two new rigorous results on the nonanalytic properties of thermodynamic potentials at first-order phase transition. For lattice models (d>or=2) with arbitrary finite state space, finite-range interactions which have two ground states, we prove that the pressure has no analytic continuation at the first-order phase-transition point, under the only further assumptions that the Peierls condition is satisfied for the ground states and that the temperature is sufficiently low. For Ising models with Kac potentials J(gamma)(x)=gamma(d)phi(gammax), where 00) and analyticity in the mean field limit (gamma SE pointing arrow 0).     

Entanglement and criticality in translationally invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with nonrandom, finite-range interactions. We show that the criticality of the system as well as validity or breakdown of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular, for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bipartite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strong evidence for the multidimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest-neighbor coupling is analyzed.     

Random Walk on the High-Dimensional IIC

We study the asymptotic behavior of the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by Kumagai and Misumi (J Theor Probab 21:910–935, 2008). We do this by getting bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander–Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.     

The classical mechanics of one-dimensional systems of infinitely many particles

We prove a global existence and uniqueness theorem for solutions of the classical equations of motion for a one-dimensional system of infinitely many particles interacting by finite-range two-body forces which satisfy a Lipschitz condition.     

Convergence of a cluster expansion for randomly dilute Ising models

We consider an Ising model with translationally invariant finite-range interactions, where a fraction p of the lattices sites is occupied by spin vectors. We prove that the expansion of the free energy in powers of p has a nonzero radius of convergence for all values of the temperature.     

Translational entanglement via collisions: how much quantum information is obtainable?

We study collisions mediated by finite-range potentials as a tool for generating translational entanglement between unbound particles or multipartite systems. The general analysis is applied to one-dimensional scattering, where resonances and the initial phase-space distribution are shown to determine the degree of postcollisional entanglement.     

Bose-Einstein condensates and Efimov states in trapped many-boson systems

We investigate trapped cold Bose gases using the stochastic variational approach with realistic attractive finite-range two-body interactions. We study the properties of the Bose-Einstein condensates, particularly in the large scattering-length regime, and establish the existence of meta-stable many-body Efimov states.     

The global minimum of energy is not always a sum of local minima—A note on frustration

A classical lattice gas model with translation-invariant, finite-range competing interactions, for which there does not exist an equivalent translation-invariant, finite-range nonfrustrated potential, is constructed. The construction uses the structure of nonperiodic ground-state configurations of the model. In fact, the model does not have any periodic ground-state configurations. However, its ground-state—a translation-invariant probability measure supported by ground-state configurations—is unique.     

Numerical calculation of strong-field laser-atom interaction: An approach with perfect reflection-free radiation boundary conditions

The time-dependent, single-particle Schrödinger equation with a finite-range potential is solved numerically on a three-dimensional spherical domain. In order to correctly account for outgoing waves, perfect reflection-free radiation boundary conditions are used on the surface of a sphere. These are computationally most effective if the particle wavefunction is expanded in the set of spherical harmonics and computations are performed in the Kramers-Henneberger accelerated frame. The method allows one to solve the full ionization dynamics in intense laser fields within a small region of atomic dimensions.     

Systematics of the first 2+ excitation with the Gogny interaction

We report the first comprehensive calculations of 2(+) excitations with a microscopic theory applicable to over 90% of the known nuclei. The theory uses a quantal collective Hamiltonian in five dimensions. The only parameters in theory are those of the finite-range, density-dependent Gogny D1S interaction. The following properties of the lowest 2(+) excitations are calculated: excitation energy, reduced transition probability, and spectroscopic quadrupole moment. We find that the theory is very reliable to classify the nuclei by shape. For deformed nuclei, average excitation energies and transition quadrupole moments are within 5% of the experimental values, and the dispersion about the averages are roughly 20% and 10%, respectively. Including all nuclei in the performance evaluation, the average transition quadrupole moment is 11% too high and the average energy is 13% too high.     

Correlation and finite interaction-range effects in high energy electron inclusive scattering

We calculate cross sections of high energy electron inclusive scattering off nuclear matter in a new and consistent formulation based on the Glauber approximation. It allows us to examine the details of the nucleon-nucleon interaction in the final-state interaction and the nuclear wave function. We point out the importance of the finite-range effect and of the nuclear short-range correlations.     

Weakly Bound Systems in the Case of Complex Potentials

We consider weakly bound two-body systems. We study the behavior of the ground state mean square radius as the binding energy tends to zero in the case of complex potentials. We show that the asymptotic law, obtained with real potentials, is modified by the occurrence of a finite width in the case of finite-range potentials. The case of the PT-symmetric potentials is also discussed. We complete our study with few remarks concerning the same problem for three weakly bound particles.     

Compact reformulation of distorted-wave and coupled-channel born approximations for transfer reactions between nuclei

DWBA and CCBA calculations are reformulated in a form which is compact, and which is symmetric with respect to the projected-ejectile system and to the target-residual nucleus system, so that the formulae can be used conveniently for heavy-ion as well as light-ion induced reactions. Clarification is also made of the relation between the exact finite-range calculations on the one hand and the no-recoil and zero-range approximations on the other. Some detailed information is given to show how to carry out efficiently the exact finite-range calculations.     

Stable Quasicrystalline Ground States

We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.     

Cluster expansion ford-dimensional lattice systems and finite-volume factorization properties

We consider classical lattice systems with finite-range interactions ind dimensions. By means of a block-decimation procedure, we transform our original system into a polymer system whose activity is small provided a suitable factorization property of finite-volume partition functions holds. In this way we extend a result of Olivieri.     

Breakdown of universality for unequal-mass Fermi gases with infinite scattering length

We treat small trapped unequal-mass two-component Fermi gases at unitarity within a nonperturbative microscopic framework and investigate the system properties as functions of the mass ratio κ, and the numbers N1 and N2 of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies s-wave scattering length a(s) are universal, we find that unequal-mass Fermi gases are, for sufficiently large κ and in the regime where Efimov physics is absent, not universal. In particular, the (N?,N?) = (2, 1) and (3, 1) systems exhibit three-body and four-body resonances at κ=12.314(2) and 10.4(2), respectively, as well as surprisingly large finite-range effects. These findings have profound implications for ongoing experimental efforts and quantum simulation proposals that utilize unequal-mass atomic Fermi gases.