相关论文: Bound-state eigenenergy outside and inside the con…

A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the…

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…

Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass…

In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…

We consider the buckling eigenvalue problem for a clamped plate in the annulus. We identify the first eigenvalue in dependence of the inner radius, and study the number of nodal domains of the corresponding eigenfunctions. Moreover, in…

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…

The current-carrying steady-state that arises in the middle of a metallic wire connected to macroscopic leads is characterized regarding its response functions, correlations and entanglement entropy. The spectral function and the dynamical…

Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. In this work, we propose a statistical ansatz for the matrix elements of non-equilibrium initial states in…

In this paper, by means of Birkhoff--Kellogg type Theorem in cones we address the existence of eigenvalues and the corresponding eigenvectors to a family of coupled system of thermostat type. The system is characterized by the presence of a…

In the present work we consider a model that has been proposed at the continuum level for self-defocusing nonlinearities in atomic BECs in order to capture phenomenologically the loss of condensate atoms to thermal ones. We explore the…

We study the linear stability of inviscid steady parallel flow of an ideal gas in a channel of finite width. Compressible isothermal two-dimensional monochromatic perturbations are considered. The eigenvalue problem governing density and…

The variance and uncertainty product of the position and momentum many-particle operators of structureless bosons interacting by a long-range inter-particle interaction and trapped in a single-well potential are investigated. In the first…

Passive states are special configurations of a quantum system which exhibit no energy decrement at the end of an arbitrary cyclic driving of the model Hamiltonian. When applied to an increasing number of copies of the initial density…

In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain…

Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and…

One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…

The Schr\"odinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and…

We investigate stability of non-equilibrium steady states of Bose-Einstein condensates with a local one-body loss in the presence of double potential barriers. We construct an exactly solvable mean-field model, in which the local loss and…