Related papers: The effect of long range interactions on the stabi…
We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The generation of entanglement between two oscillators that interact via a common reservoir is theoretically studied. The reservoir is modeled by a one-dimensional harmonic crystal initially in thermal equilibrium. Starting from a separable…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
Quantum-classical transitions have long attracted much attention. We study such transitions in quantum spin-($j$,1/2) systems at thermal equilibrium. Unlike the previous work [Phys. Rev. A 73, 064302 (2006)], it is found that the threshold…
A two-dimensional topologically ordered quantum memory is well protected against error if the energy gap is large compared to the temperature, but this protection does not improve as the system size increases. We review and critique some…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-\alpha} at large distances r with an exponent $\alpha$ not exceeding the lattice dimension. For a large class of…
We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau…
The "melting" of self-formed rigid structures made of a small number of interacting classical particles confined in an irregular two-dimensional space is investigated using Monte Carlo simulations. It is shown that the interplay of…
We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings which decrease with distance as $r^{-\alpha}$ ($\alpha \ge 0$), subject at its ends to Brownian heat reservoirs at…
Monte Carlo simulations are used to show that the steady state of the d=2, two-temperature, diffusive XY model displays a continuous phase transition from a homogeneous disordered phase to a phase with long-range order. The long-range order…
We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power $\alpha$…
We study a quantum oscillator interacting and back-reacting on a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system…
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction.…
The Lieb-Schultz-Mattis (LSM) theorem asserts that microscopic details of the system can impose non-trivial constraints on the system's low-energy properties. While traditionally applied to short-range interaction systems, where locality…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
The van der Waals-London's law, for a collection of atoms at large separation, states that their interaction energy is pairwise attractive and decays proportionally to one over their distance to the sixth. The first rigorous result in this…
The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a…
We consider an electron-phonon system in two and three dimensions on square, hexagonal and cubic lattices. The model is a modification of the standard Holstein model where the optical branch is appropriately curved in order to have a…