Related papers: Calculating Quantum Transports Using Periodic Boun…
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The…
We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
In this paper, we present quantum algorithms for a class of highly-oscillatory transport equations, which arise in semiclassical computation of surface hopping problems and other related non-adiabatic quantum dynamics, based on the…
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
To apply the scattering approach for the problem of AC transport through coherent quantum conductors, various partial density of states must be evaluated. If the global partial density of states (GPDOS) is calculated externally using the…
We analyze the precision of currents in a generic multi-terminal quantum-transport setting. Employing scattering theory, we show that the precision of the currents is limited by a function of the particle-current noise that can be…
We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
We approach the problem of constructing a quantum analogue of the immensely fruitful classical transport cost theory of Monge from a new angle. Going back to the original motivations, by which the transport is a bilinear function of a mass…
Starting with the many-body Schr\"odinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
A user friendly scheme based on the quantum kinetic equation is developed for studying thermal transport phenomena in the presence of interactions and disorder. We demonstrate that this scheme is suitable for both a systematic perturbative…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…