|
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] |
Models Osc
A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the universe, physical or human condition, human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dissipation
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] |
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] |
The 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] |
Quantum Dissipation
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] |
The 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] |
