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Hierarchical Equations Of Motion
The hierarchical equations of motion (HEOM) technique derived by Yoshitaka Tanimura and Ryogo Kubo in 1989, is a non-perturbative approach developed to study the evolution of a density matrix \rho(t) of quantum dissipative systems. The method can treat system-bath interaction non-perturbatively as well as non-Markovian noise correlation times without the hindrance of the typical assumptions that conventional Redfield (master) equations suffer from such as the Born, Markovian and rotating-wave approximations. HEOM is applicable even at low temperatures where quantum effects are not negligible. The hierarchical equation of motion for a system in a harmonic Markovian bath is : \frac_n = - (\frac\hat^_A + n\gamma) \hat_n - \hat^\hat_ + \hat\hat_ Hierarchical equations of motion HEOMs are developed to describe the time evolution of the density matrix \rho(t) for an open quantum system. It is a non-perturbative, non-Markovian approach to propagating in time a quantum state. Motivate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoshitaka Tanimura
is a Japanese mathematical physicist, best known for his invention with Ryogo Kubo of the Hierarchical equations of motion. In 1993, while working at University of Rochester with Shaul Mukamel, he published a theoretical paper laying the foundation for (optical) two-dimensional femtosecond spectroscopies. See also * Hierarchical equations of motion References {{DEFAULTSORT:Tanimura, Yoshitaka Japanese physicists Academic staff of Kyoto University Keio University alumni Living people 1960 births Fellows of the American Physical Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ryogo Kubo
was a Japanese mathematical physicist, best known for his works in statistical physics and non-equilibrium statistical mechanics. Work In the early 1950s, Kubo transformed research into the linear response A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in informatio ... properties of near-equilibrium condensed-matter systems, in particular the understanding of electron transport and conductivity, through the Kubo formalism, a Green's function approach to linear response theory for quantum systems. In 1977 Ryogo Kubo was awarded the Boltzmann Medal ''for his contributions to the theory of non-equilibrium statistical mechanics, and to the theory of fluctuation phenomena''. He is cited particularly for his work in the establishment of the basic relations between transport coefficients and eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Quantum System
In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the ''environment'' or a ''bath''. In general, these interactions significantly change the dynamics of the system and result in quantum dissipation, such that the information contained in the system is lost to its environment. Because no quantum system is completely isolated from its surroundings, it is important to develop a theoretical framework for treating these interactions in order to obtain an accurate understanding of quantum systems. Techniques developed in the context of open quantum systems have proven powerful in fields such as quantum optics, quantum measurement theory, quantum statistical mechanics, quantum information science, quantum thermodynamics, quantum cosmology, quantum biology, and semi-classical approximations. Quantum system and environment A complete description of a quantum system requires the inclusion of the environment. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bytes
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol () refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness. The first bit is number 0, making the eighth bit number 7. The size of the byte has historically been hardware-dependent and no definitive standards existed that mandated the size. Sizes from 1 to 48 bits have been used. The six-bit character code was an often-used implementation in early encoding systems, and computers using six-bit and nine-bit bytes were common in the 1960s. These systems often had memory words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NanoHUB
nanoHUB.org is a science and engineering gateway comprising community-contributed resources and geared toward education, professional networking, and interactive simulation tools for nanotechnology. Funded by the United States National Science Foundation (NSF), it is a product of the Network for Computational Nanotechnology (NCN). NCN supports research efforts in nanoelectronics; nanomaterials; nanoelectromechanical systems (NEMS); nanofluidics; nanomedicine, nanobiology; and nanophotonics. History The Network for Computational Nanotechnology was established in 2002 to create a resource for nanoscience and nanotechnology via online services for research, education, and professional collaboration. Initially a multi-university initiative of eight member institutions including Purdue University, the University of California at Berkeley, the University of Illinois at Urbana-Champaign, Massachusetts Institute of Technology, the Molecular Foundry at Lawrence Berkeley National Laborator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klaus Schulten
Klaus Schulten (January 12, 1947 – October 31, 2016) was a German-American computational biophysicist and the Swanlund Professor of Physics at the University of Illinois at Urbana-Champaign. Schulten used supercomputing techniques to apply theoretical physics to the fields of biomedicine and bioengineering and dynamically model living systems. His mathematical, theoretical, and technological innovations led to key discoveries about the motion of biological cells, sensory processes in vision, animal navigation, light energy harvesting in photosynthesis, and learning in neural networks. Schulten identified the goal of the life sciences as being to characterize biological systems from the atomic to the cellular level. He used petascale computers, and planned to use exa-scale computers, to model atomic-scale bio-chemical processes. His work made possible the dynamic simulation of the activities of thousands of proteins working together at the macromolecular level. His ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Master Equation
A quantum master equation is a generalization of the idea of a master equation. Rather than just a system of differential equations for a set of probabilities (which only constitutes the diagonal elements of a density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical. Off-diagonal elements represent quantum coherence which is a physical characteristic that is intrinsically quantum mechanical. A formally exact quantum master equation is the Nakajima–Zwanzig equation, which is in general as difficult to solve as the full quantum problem. The Redfield equation and Lindblad equation are examples of approximate Markov property, Markovian quantum master equations. These equations are very easy to solve, but are not generally accurate. Some modern approx ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Quantum System
In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the ''environment'' or a ''bath''. In general, these interactions significantly change the dynamics of the system and result in quantum dissipation, such that the information contained in the system is lost to its environment. Because no quantum system is completely isolated from its surroundings, it is important to develop a theoretical framework for treating these interactions in order to obtain an accurate understanding of quantum systems. Techniques developed in the context of open quantum systems have proven powerful in fields such as quantum optics, quantum measurement theory, quantum statistical mechanics, quantum information science, quantum thermodynamics, quantum cosmology, quantum biology, and semi-classical approximations. Quantum system and environment A complete description of a quantum system requires the inclusion of the environment. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fokker–Planck Equation
In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as well. It is named after Adriaan Fokker and Max Planck, who described it in 1914 and 1917. It is also known as the Kolmogorov forward equation, after Andrey Kolmogorov, who independently discovered it in 1931. When applied to particle position distributions, it is better known as the Smoluchowski equation (after Marian Smoluchowski), and in this context it is equivalent to the convection–diffusion equation. The case with zero diffusion is the continuity equation. The Fokker–Planck equation is obtained from the master equation through Kramers–Moyal expansion. The first consistent microscopic derivation of the Fokker–Planck equation in the sing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dynamical Semigroup
In quantum mechanics, a quantum Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first introduced by A. M. Kossakowski in 1972, and then developed by V. Gorini, A. M. Kossakowski, E. C. G. Sudarshan and Göran Lindblad in 1976. Motivation An ideal quantum system is not realistic because it should be completely isolated while, in practice, it is influenced by the coupling to an environment, which typically has a large number of degrees of freedom (for example an atom interacting with the surrounding radiation field). A complete microscopic description of the degrees of freedom of the environment is typically too complicated. Hence, one looks for simpler descriptions of the dynamics of the open system. In principle, one should investigate the unitary dynamics of the total system, i.e. the system and the environment, to obtain information about the reduced system of interest by av ... [...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] |
