Related papers: Landauer-B\"uttiker formula and Schr\"odinger conj…
We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle. Despite its model and rather abstract character this question is worth…
We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within…
We examine the quantum entanglement spectra and Wannier functions of the square lattice Hofstadter model. Consistent with previous work on entanglement spectra of topological band structures, we find that the entanglement levels exhibit a…
We analyze Landauer's principle for repeated interaction systems consisting of a reference quantum system $\mathcal{S}$ in contact with an environment $\mathcal{E}$ which is a chain of independent quantum probes. The system $\mathcal{S}$…
We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
We propose a formalism which uses boundary conditions imposed on the Luttinger liquid (LL) to describe the transport properties of a LL coupled to reservoirs. The various boundary conditions completely determine linear transport in the…
The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…
A general argument leading from the formula for currents through an open noninteracting mesoscopic system given by the theory of non-equilibrium steady states (NESS) to the Landauer-Buettiker formula is pointed out. Time reversal symmetry…
The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…
The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum…
The reciprocal Schr\"{o}dinger equation $\partial S(\omega ,{\bf r}% )/i\partial \omega =\hat{\tau}(\omega ,{\bf r}) S(\omega ,{\bf r})$ for $S$-matrix with temporal operator instead the Hamiltonian is established via the Legendre…
A linearized Vlasov-Poisson system of equations is transformed into a Schr\"{o}dinger equation, which is used to demonstrate that the fluctuation theorem holds for the relative stochastic entropy, defined in terms of the probability density…
The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a non-interacting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small…
We prove the existence of ballistic transport for the Schr\"odinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior…
We explore the effect of local constraints on one-dimensional bosonic and fermionic ground state phases. Motivated by recent experiments on Rydberg chains, we constrain the occupation of neighboring sites in known phases of matter. Starting…
We study the scattering properties of Schr\"{o}dinger operators with bounded potentials concentrated near a subspace of $\mathbb{R}^d$. For such operators, we show the existence of scattering states and characterize their orthogonal…
We compute the entanglement entropy and the entanglement spectrum of the vacuum state in the massive Schwinger model at a finite $\theta$ angle. The $\theta$ term is implemented through a chirally rotated lattice Hamiltonian that preserves…