Related papers: Random-Matrix Approach to Transition-State Theory

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer, but to design a suitable one. We are particularly interested…

We study the decay of general initial states out of a metastable potential well in quantum mechanics. We provide a closed-form expression for the probability current that tunnels through the barrier in terms of the resonant states into…

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…

We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical…

Tunneling through a localized barrier in a one-dimensional interacting electron gas has been studied recently using Luttinger liquid techniques. Stable phases with zero or unit transmission occur, as well as critical points with universal…

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with…

Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…

Quantum tunneling from a thin wire or a thin film through a static potential barrier in a zero magnetic field is studied. The wire or the film should satisfy a condition of transverse quantization of levels and be inhomogeneous. Depending…

We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…

The transfer Hamiltonian tunneling current is derived in a time-dependent density matrix formulation and is used to examine photon-assisted tunneling. Bardeen's tunneling expression arises as the result of first order perturbation theory in…

Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…

Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…

Quantum transition probabilities and quantum entanglement for two-qubit states of a four level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a…

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…

The tunneling hamiltonian has proven to be a useful method in many body physics to treat particle tunneling between different states represented as wavefunctions. Our problem is here applying what we did in the first paper to a driven…

We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…

For a non-superconducting system, the electronic tunneling current through an insulating barrier is calculated, including interaction effects. The exact Hamiltonian of the full system is projected onto the subspaces of the "left" and…