A mesoscopic evolution equation for an ensemble of mesoparticles follows from the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales then the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling between the system, defined by mesoscopic variables, and internal degrees of freedom. We briefly discuss the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.
A mesoscopic evolution equation for an ensemble of mesoparticles follows from the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales then the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling between the system, defined by mesoscopic variables, and internal degrees of freedom. We briefly discuss the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.
The Lindblad master equation governs the general Markovian evolution of a density operator for an open quantum system. Semiclassical Wigner functions represent density operators in phase space in terms of chords on a classical manifold, so that the amplitude and phase of each chord contribution is classically defined. Inserting such a Wigner function into a phase space version of the master equation, its explicit evolution is derived in the absence of dissipation. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude exponentially. Projecting the Wigner function on to an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.
We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.
In this paper, we consider a system with both translational degrees of freedom and a structure of discrete internal states. Applying a multiple-time-scale approach we can separate the dynamical processes describing internal quantum transitions between the states and semiclassical propagation in phase space. The freedom provided by the multiple-time-scale method seems to offer the possibility of carrying out such a separation without internal contradictions. The case with no internal states is extracted and compared with other semiclassical results in the literature; it is found that our approach can be related to these, but it is not identical with any previously reported results. When a unique particle trajectory can be defined, the procedure is shown to lead to the customary classical-path approximation often employed in scattering theory and quantum optics. This approach is generalized into a self-consistent method, but it is not expected to be applicable in the coherence-destroying case with widely separated trajectories for the internal states. The validity of the approach and its limitations are discussed.
The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Bañuls M C and Pérez A 2012 New J. Phys.14 103009) is extended here to include an internal degree of freedom as spin.This extension is made by introducing a Wigner matrix.The formalism is developed to account for dynamical processes, with or without decoherence.We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited.Discrete processes are also discussed.Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Bañuls M C and Pérez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
Explanation of decoherence and quasi-equilibrium in systems with few degrees of freedom demands a deep theoretical analysis that considers the observed system as an open quantum system. In this work, we study the problem of decoherence of an observed system of quantum interacting particles, coupled to a quantum lattice. Our strategy is based on treating the environment and the system-environment Hamiltonians fully quantum mechanically, which yields a representation of the time evolution operator useful for disentangling the different time scales underlying in the observed system dynamics. To describe the possible different stages of the dynamics of the observed system, we introduce quantum mechanical definitions of essentially isolated, essentially adiabatic, and thermal-contact system-environment interactions. This general approach is then applied to the study of decoherence and quasi-equilibrium in proton nuclear magnetic resonance ((1)H NMR) of nematic liquid crystals. A summary of the original results of this work is as follows. We calculate the decoherence function and apply it to describe the evolution of a coherent spin state, induced by the coupling with the molecular environment, in absence of spin-lattice relaxation. By assuming quantum energy conserving or non-demolition interactions, we identify an intermediate time scale, between those controlled by self-interactions and thermalization, where coherence decays irreversibly. This treatment is also adequate for explaining the buildup of quasi-equilibrium of the proton spin system, via the process we called eigen-selectivity. By analyzing a hypothetical time reversal experiment, we identify two sources of coherence loss which are of a very different nature and give rise to distinct time scales of the spin dynamics: (a) reversible or adiabatic quantum decoherence and (b) irreversible or essentially adiabatic quantum decoherence. Local irreversibility arises as a consequence of the uncertainty introduced by the coupling with an infinite quantum environment. The reversible part can be represented by a semiclassical model, similar to standard line-shape adiabatic models. By exploiting the separation existing between the time scales of the spin coherences and the irreversible decoherence, we present a novel technique to obtain the orientational molecular distribution function for a nematic liquid crystal. The procedure is based on the comparison of the observed coherence time evolution and numerical calculation under the adiabatic quantum decoherence approach. As an example, it is used the experimental free induction decay from a nematic PAA(d6) sample to extract such an orientational distribution. This is the first theoretical description of the experimental liquid crystal NMR signal in the time domain. On the contrary, the irreversible decoherence is intrinsically full-quantum mechanical, as it is governed by the commutation properties of the environment and the spin-lattice Hamiltonians. Consistently, it depends on the molecular correlation in a decisive way, since it vanishes under a mean-field model for the molecular dynamics. The results of this work can contribute to the understanding of the open question of the applicability of the spin-temperature concept in spin systems with few degrees of freedom.