arXiv subjects

Jeremy B. Maddox

Publications and source records attributed to Jeremy B. Maddox.

3 recordsLinked to original sources

arXiv2009

A Supersymmetric Approach to Excited States via Quantum Monte Carlo

We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrödinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.

hep-th↗

arXiv2008

Single-electron counting spectroscopy: simulation study of porphyrin in a molecular junction

Electron counting of a single porphyrin molecule between two electrodes shows a crossover from sub- to super-Poissonian statistics as the bias voltage is scanned. This is attributed to the simultaneous activation of states with electron transfer rates spanning several orders of magnitude. Time-series analysis of consecutive single electron transfer events reveals fast and slow transport channels, which are not resolved by the average current alone.

cond-mat.mes-hall↗

arXiv2001

Quantum Liouville-space trajectories for dissipative systems

In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum equations-of-motion for Liouville-space trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and non-local quantum potential which continuously produces coherences in the system. These trajectories are then used to propagate an adaptive Lagrangian grid which carries the density matrix, $ρ(x,y)$, and the action, $A(x,y)$, thereby providing a complete hydrodynamic-like description of the dynamics.

quant-ph↗