Recently, time-dependent current-density-functional theory has been extended to include the dynamical interaction of quantum systems with external environments (Di Ventra and D'Agosta 2007 Phys.Rev. Lett.98 226403).Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems.As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the context of quantum measurement theory.
Recently, time-dependent current-density-functional theory has been extended to include the dynamical interaction of quantum systems with external environments (Di Ventra and D'Agosta 2007 Phys.Rev. Lett.98 226403).Here we show that such a theory allows us to study a fundamentally important class of phenomena previously inaccessible by standard density-functional methods: the decay of excited systems.As an example we study the decay of an ensemble of excited He atoms, and discuss these results in the context of quantum measurement theory.
The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. 98, 226403 (2007)], which allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density-matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion and apply this theory to the dynamics of a one-dimensional gas of excited bosons confined in a harmonic potential and in contact with an external bath.
A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state |Psi0> and the particle-bath interaction operator, two external vector potentials A(r,t) and A'(r,t) that produce the same ensemble-averaged current density, j(r,t), must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.
A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state j 0i and the particle-bath interaction operator, two external vector potentials A r; t and A0 r; t that produce the same ensemble-averaged current density, j r; t , must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.
Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some crucial parts of the theory of stochastic processes (the proper context in which to discuss dynamics), and develop a general framework for specifying a dynamics for density operator interpretations. This framework admits infinitely many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them.