相关论文: 13-Moment System with Global Hyperbolicity for Qua…
In this paper we study global existence of weak solutions for the Quantum Hydrodynamics System in 2-D in the space of energy. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach…
This work deals with the physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential in the context of…
Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the…
In this paper, we investigate the initial value problem for symmetric hyperbolic systems on globally hyperbolic Lorentzian manifolds with potentials that are both nonlocal in time and space. When the potential is retarded and uniformly…
We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
In this article, we investigate the maximal smoothness (infinite differentiability) of solutions to thermoelastic models, specifically those where the heat equation is of the ``phase-lag'' or ``parabolic'' type. We derive optimal regularity…
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schr\"odinger's equation and the second law of thermodynamics. Despite…
The global dynamics and regularity of parabolic-hyperbolic systems is an interesting topic in PDEs due to the coupling of competing dissipation and hyperbolic effects. This paper is concerned with the Cauchy problem of a…
Asymptotically flat gravitating systems have 10 conserved quantities, which lack proper local densities. It has been hoped that the teleparallel equivalent of Einstein's GR (TEGR, aka GR${}_{||}$) could solve this gravitational…
This paper performs a stability analysis of a class of moment closure systems derived with an extended quadrature method of moments (EQMOM) for the one-dimensional BGK equation. The class is characterized with a kernel function. A…
We propose a new representation for several quantum master equations in so-called quasithermodynamic form. This representation (when it exists) let one to write down dynamical equations both for diagonal and non-diagonal elements of density…
A (globally) neutral two-body system is supposed to obey a pair of coupled Klein-Gordon equations in a constant homogeneous magnetic field. Considering eigenstates of the pseudomomentum four-vector, we reduce these equations to a…
In this paper, we are concerned with the instability and stability of a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the pressure satisfies $\frac{\nu P'(\bar\rho)}{\gamma \bar\rho} <…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
We study 2-local Hamiltonian quantum systems, consisting of qubits interacting on the star graph of N vertices. We numerically demonstrate that these models are generically non-integrable at infinite temperature, and find evidence for a…
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSS) whose lifetime increases with the system size. In the paradigmatic Hamiltonian Mean-field Model (HMF) out-of-equilibrium phase…
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full…