Related Research Articles
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of Planck's constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos. If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?
In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation, master equation in Lindblad form, quantum Liouvillian, or Lindbladian is the most general type of Markovian and time-homogeneous master equation describing evolution of the density matrix ρ that preserves the laws of quantum mechanics.
A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. For comparison of the models proposed in these papers see M. I. Dykman and E. I. Rashba, The roots of polaron theory, Physics Today 68, 10 (2015). This lowers the electron mobility and increases the electron's effective mass.
In physics, chemistry and related fields, master equations are used to describe the time evolution of a system that can be modelled as being in a probabilistic combination of states at any given time and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states.
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.
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.
Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and many other phenomena governed by Einstein's theory of general relativity. A currently active field of research in numerical relativity is the simulation of relativistic binaries and their associated gravitational waves. Other branches are also active.
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution of the quantum many-body problem. The diverse flavor of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. The quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory and offering an exact solution of the many-body problem in some circumstances. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems and discrete systems. The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them with motif.
The classical-map hypernetted-chain method is a method used in many-body theoretical physics for interacting uniform electron liquids in two and three dimensions, and for non-ideal plasmas. The method extends the famous hypernetted-chain method (HNC) introduced by J. M. J van Leeuwen et al. to quantum fluids as well. The classical HNC, together with the Percus–Yevick approximation, are the two pillars which bear the brunt of most calculations in the theory of interacting classical fluids. Also, HNC and PY have become important in providing basic reference schemes in the theory of fluids, and hence they are of great importance to the physics of many-particle systems.
In physics, the Bethe ansatz is an ansatz method for finding the exact wavefunctions of certain one-dimensional quantum many-body models. It was invented by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic Heisenberg model Hamiltonian. Since then the method has been extended to other models in one dimension: the (anisotropic) Heisenberg chain, the Lieb-Liniger interacting Bose gas, the Hubbard model, the Kondo model, the Anderson impurity model, the Richardson model etc.
The Sudarshan-Glauber P representation is a suggested way of writing down the phase space distribution of a quantum system in the phase space formulation of quantum mechanics. The P representation is the quasiprobability distribution in which observables are expressed in normal order. In quantum optics, this representation, formally equivalent to several other representations, is sometimes championed over alternative representations to describe light in optical phase space, because typical optical observables, such as the particle number operator, are naturally expressed in normal order. It is named after George Sudarshan and Roy J. Glauber, who worked on the topic in 1963. Despite many useful applications in laser theory and coherence theory, the Glauber–Sudarshan P representation has the drawback that it is not always positive, and is not a true probability function.
Car–Parrinello molecular dynamics or CPMD refers to either a method used in molecular dynamics or the computational chemistry software package used to implement this method.
The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a diabatic transition between the two energy states, was published separately by Lev Landau, Clarence Zener, Ernst Stueckelberg, and Ettore Majorana, in 1932.
The Nakajima–Zwanzig equation is an integral equation describing the time evolution of the "relevant" part of a quantum-mechanical system. It is formulated in the density matrix formalism and can be regarded a generalization of the master equation.
The quantum jump method, also known as the Monte Carlo wave function (MCWF) is a technique in computational physics used for simulating open quantum systems and quantum dissipation. The quantum jump method was developed by Dalibard, Castin and Mølmer at a similar time to the similar method known as Quantum Trajectory Theory developed by Carmichael. Other contemporaneous works on wave-function-based Monte Carlo approaches to open quantum systems include those of Dum, Zoller and Ritsch and Hegerfeldt and Wilser.
Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905, Albert Einstein argued that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized obtaining the relation . This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition, there is a quest for the theory to be relevant for a single individual quantum system.
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 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.
Sudhir Ranjan Jain(16 May 1963) is an Indian theoretical physicist at Bhabha Atomic Research Centre, Mumbai, known for his contributions in complex quantum systems and Nonlinear dynamics. He is a scientist at the nuclear physics division of Bhabha Atomic Research Centre, professor at Homi Bhabha National Institute and adjunct professor at the Centre for Excellence in Basic Sciences. He authored Mechanics, Waves and Thermodynamics: An Example-based Approach. His doctoral advisor was Prof. Suresh V. Lawande who was a student of Edward Teller. Prof. Lawande is known for his contributions in developing Monte Carlo methods in the evaluation of Feynman path integrals in imaginary time.
References
- ↑ D. McCutcheon, N. S. Dattani, E. Gauger, B. Lovett, A. Nazir (25 August 2011). "A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots". Physical Review B. 84 (8): 081305R. arXiv: 1105.6015 . Bibcode:2011PhRvB..84h1305M. doi:10.1103/PhysRevB.84.081305. S2CID 119275166.CS1 maint: multiple names: authors list (link)
- ↑ Dattani, Nike (2013), "FeynDyn: A MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs", Computer Physics Communications, 184 (12): 2828–2833, arXiv: 1205.6872 , Bibcode:2013CoPhC.184.2828D, doi:10.1016/j.cpc.2013.07.001, S2CID 41378038
- ↑ Prior, Javier (30 July 2010). "Efficient Simulation of Strong System-Environment Interactions". Phys. Rev. Lett. 105: 050404. doi:10.1103/PhysRevLett.105.050404 . Retrieved 2 June 2021.
- ↑ Wang, Haobin (24 March 2017). "A multilayer multiconfiguration time-dependent Hartree simulation of the reaction-coordinate spin-boson model employing an interaction picture". J. Chem. Phys. 146: 124112. doi:10.1063/1.4978901 . Retrieved 2 June 2021.