Related papers: Some remarks about quantum diffusion for Hubbard m…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…
The evolution of the ground state and the excitation spectrum of the two and three dimensional attractive Hubbard model is studied as the system evolves from a Cooper pair regime for weak attraction to a composite boson regime for a strong…
It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low…
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin…
Nonlinear and nonlinear evolution equations of the form $u_t=\L u \pm|\nabla u|^q$, where $\L$ is a pseudodifferential operator representing the infinitesimal generator of a L\'evy stochastic process, have been derived as models for growing…
Experiments with polymer latex solutions show the coexistence of order-disorder structures of macroions. Because of the large macroions' sizes, this order-disorder phase coexistence imply the existence of very long-range attractive and…
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or…
We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…
Even though the Hubbard model is one of the most fundamental models of highly correlated electrons, analytical and numerical data describing its thermodynamics at nonzero magnetization are relatively scarce. We present a detailed…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized…
We derive uniform in time $L^\infty$-bound for solutions to an aggregation-diffusion model with attractive-repulsive potentials or fully attractive potentials. We analyze two cases: either the repulsive nonlocal term dominates over the…
We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and…
Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect.…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
We investigate universal properties of one-dimensional multi-component systems comprised of fermions, bosons, or an arbitrary mixture, with contact interactions and subjected to an external potential. The masses and the coupling strengths…
Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special…