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We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against…
How environments affect dynamics of quantum systems remains a central question in understanding transitions between quantum and classical phenomena and optimizing quantum technologies. A paradigm model to address the above question is the…
Based on recently derived exact stochastic Liouville-von Neumann equations, several strategies for the efficient simulation of open quantum systems are developed and tested on the spin-boson model. The accuracy and efficiency of these…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power…
We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known…
We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and…
We develop a method for finding the time evolution of exactly solvable models by Bethe ansatz. The dynamical Bethe wavefunction takes the same form as the stationary Bethe wavefunction except for time varying Bethe parameters and a complex…
The time-global existence of unique smooth positive solutions to the reaction diffusion equations of the Keener-Tyson model for the Belousov-Zhabotinsky reaction in the whole space is established with bounded non-negative initial data.…
The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…
We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. Potential is replaced by offshell bosonic quanta inside the bound state of…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…
Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as…
We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ an hydrodynamic parametrization of the…
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…
In the framework of Heisenberg-Langevin theory the dynamical and statistical effects arising from the linear interaction of two nondegenerate down-conversion processes are investigated. Using the strong-pumping approximation the analytical…