Abstract
A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrödinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction (linked to the corresponding Bohmian trajectory) as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends to the quantum regime, the computational capabilities that the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.
Highlights
Thanks to its accuracy and versatility, the Monte Carlo solution of the Boltzmann transport equation has been, for decades, the preferred computational tool to predict the DC, AC, transient, and noise performances of semi-classical electron devices [1]
Theoretical approaches to open quantum systems that rely on the manipulation of state vectors instead of a reduced density matrix have well known computational advantages
For example, that the continuous measurement of an open quantum system with associated Markovian dynamics can be described by means of a stochastic Schrödinger equation (SSE)
Summary
Thanks to its accuracy and versatility, the Monte Carlo solution of the Boltzmann transport equation has been, for decades, the preferred computational tool to predict the DC, AC, transient, and noise performances of semi-classical electron devices [1]. Instead of directly solving equations of motion for the reduced density matrix, the SSE approach exploits the state vector nature of the so-called conditional states to alleviate some computational burden (and ensure a complete positive map by construction [18]) Even if this technique allows to always reconstruct the full density matrix, a discussion on whether dynamical information can be directly extracted from such conditional states in non-Markovian scenarios has appeared recently in the literature [19,20]. This debate is very relevant to us as we are interested in computing one-time expectation values (i.e., DC performance) and dynamical properties (i.e., AC, transient, and noise), such as multi-time correlation functions, at THz frequencies.
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