相关论文: About classical solutions of the path-dependent he…
We analyze the equations governing the evolution of distributions of the work and the heat exchanged with the environment by a manipulated stochastic system, by means of a compact and general derivation. We obtain explicit solutions for…
By a probabilistic method we provide an explicit fundamental solution of the Cauchy problem associated to the heat equation on the half-line with constant drift and Dirichlet boundary condition at zero.
We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola…
We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
Starting from Schr\"odinger's equation, Hamilton's classical equations of motion emerge from the collapse of the unsymmetrized wave function in a decoherent open quantum system entangled with its environment.
Starting from the Caldeira-Leggett (CL) model, we derive the equation describing the Quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms.…
We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of Constantin-E-Titi and…
In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination…
In the present paper, we consider in detail the aspects of the Heisenberg's equations of motion, related to their transformation to the representation dependent of external sources. We provide with a closed solution as to the…
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…
In this work, surface diffusion is studied with a different perspective by showing how the corresponding open dynamics is transformed when passing, in a continuous and smooth way, from a pure quantum regime to a full classical regime; the…
We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with…
We show that the high temperature behavior of non-commutative QED may be simply obtained from Boltzmann transport equations for classical particles. The transport equation for the charge neutral particle is shown to be characteristically…
We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of…
In this paper, we study the gradient estimates of Li-Yau-Hamilton type for positive solutions to both drifting heat equation and the simple nonlinear heat equation problem $$ u_t-\Delta u=au\log u, \ \ u>0 $$ on the compact Riemannian…
In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak…
We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion.…