Related papers: Schroedinger equation for current carrying states
It has long been known that quantum particles moving in a periodic lattice and subject to a constant force field undergo an oscillatory motion that is referred to as Bloch Oscillations (BOs). However, it is also known that, under quite…
Electron transport is theoretically investigated in a molecular device made of anthracene molecule attached to the electrodes by thiol end groups in two different configurations (para and meta, respectively). Molecular system is described…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
Novel categories of electronic devices and quantum materials are obtained by pipelining the unitary evolution of electron quantum states as described by Schroedinger's equation with non-unitary processes that interrupt the coherent…
The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading…
The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t)…
In this paper we study the semiclassical limit of the Schr\"odinger equation. Under mild regularity assumptions on the potential $U$ which include Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
Nonequilibrium transport properties are determined exactly for an adiabatically connected single channel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter $g$, for very strong interactions…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
We develop an exact quantum thermodynamic description for a noninteracting nanoscale steady state that couples strongly with multiple reservoirs. It is demonstrated that there exists a steady-state extension of the thermodynamic function…
The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a…
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…
A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance…
We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the…
Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
Electron transport through a single-level quantum dot weakly coupled to Luttinger liquid leads is considered in the master equation approach. It is shown that for a weak or moderately strong interaction the differential conductance…