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Dephasing Rate SP Formula
The ''SP'' formula for the dephasing rate \Gamma_ of a particle that moves in a fluctuating environment unifies various results that have been obtained, notably in condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ..., with regard to the motion of electrons in a metal. The general case requires to take into account not only the temporal correlations but also the spatial correlations of the environmental fluctuations. These can be characterized by the spectral form factor \tilde(q,\omega), while the motion of the particle is characterized by its power spectrum \tilde(q,\omega). Consequently, at finite temperature the expression for the dephasing rate takes the following form that involves ''S'' and ''P'' functions: \Gamma_ \ = \ \int d \int \frac \,\tilde(,\om ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dephasing
In physics, dephasing is a mechanism that recovers classical behaviour from a quantum system. It refers to the ways in which coherence caused by perturbation decays over time, and the system returns to the state before perturbation. It is an important effect in molecular and atomic spectroscopy, and in the condensed matter physics of mesoscopic devices. The reason can be understood by describing the conduction in metals as a classical phenomenon with quantum effects all embedded into an effective mass that can be computed quantum mechanically, as also happens to resistance that can be seen as a scattering effect of conduction electrons. When the temperature is lowered and the dimensions of the device are meaningfully reduced, this classical behaviour should disappear and the laws of quantum mechanics should govern the behavior of conducting electrons seen as waves that move ballistically inside the conductor without any kind of dissipation. Most of the time this is what one o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi's Golden Rule
In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of a weak perturbation. This transition rate is effectively independent of time (so long as the strength of the perturbation is independent of time) and is proportional to the strength of the coupling between the initial and final states of the system (described by the square of the matrix element of the perturbation) as well as the density of states. It is also applicable when the final state is discrete, i.e. it is not part of a continuum, if there is some decoherence in the process, like relaxation or collision of the atoms, or like noise in the perturbation, in which case the density of states is replaced by the reciprocal of the decoherence bandwidth. General Although the rule is named after Enrico Fermi, most of the work leading to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dissipation Model For Extended Environment
A unified model for ''Diffusion Localization and Dissipation'' (DLD), optionally termed ''Diffusion with Local Dissipation'', has been introduced for the study of ''Quantal Brownian Motion'' (QBM) in dynamical disorder. It can be regarded as a generalization of the familiar Caldeira-Leggett model. \mathcal = \frac + V(x) + \mathcal_ + \mathcal_ \mathcal_=\sum_\left(\frac +\frac m \omega_^2 Q_^2\right) \mathcal_ = - \sum_ c_ Q_ u(x-x_) where Q_ denotes the dynamical coordinate of the \alpha scatterer or bath mode. u(x-x_) is the interaction potential, and c_ are coupling constants. The spectral characterization of the bath is analogous to that of the Caldeira-Leggett model: \frac \sum_ \frac \delta(\omega-\omega_) \ \delta(x-x_) \ = \ J(\omega) i.e. the oscillators that appear in the Hamiltonian are distributed uniformly over space, and in each location have the same spectral distribution J(\omega). Optionally the environment is characterized by the power spectrum of the fluc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caldeira-Leggett Model
Quantum dissipation is the branch of physics that studies the quantum analogues of the process of irreversible loss of energy observed at the classical level. Its main purpose is to derive the laws of classical dissipation from the framework of quantum mechanics. It shares many features with the subjects of quantum decoherence and quantum theory of measurement. Models The typical approach to describe dissipation is to split the total system in two parts: the quantum system where dissipation occurs, and a so-called environment or bath where the energy of the former will flow towards. The way both systems are coupled depends on the details of the microscopic model, and hence, the description of the bath. To include an irreversible flow of energy (i.e., to avoid Poincaré recurrences in which the energy eventually flows back to the system), requires that the bath contain an infinite number of degrees of freedom. Notice that by virtue of the principle of universality, it is expected t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
