A new form of the redfield equation for dissipative systems related to the matrix of correlation functions

2009 ◽  
Vol 161 (1) ◽  
pp. 1393-1402 ◽  
Author(s):  
I. O. Glebov ◽  
V. V. Eremin
Author(s):  
Jean Zinn-Justin

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.


2020 ◽  
Vol 17 (06) ◽  
pp. 2050090 ◽  
Author(s):  
Jordi Gaset ◽  
Xavier Gràcia ◽  
Miguel C. Muñoz-Lecanda ◽  
Xavier Rivas ◽  
Narciso Román-Roy

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.


Author(s):  
Hossein Nejat Pishkenari ◽  
Amir Lotfi Gaskarimahalle ◽  
Seyed Babak Ghaemi Oskouei ◽  
Ali Meghdari

In this paper we have presented a new form of Kane’s equations. This new form is expressed in the matrix form with the components of partial derivatives of linear and angular velocities relative to the generalized speeds and generalized coordinates. The number of obtained equations is equal to the number of degrees of freedom represented in a closed form. Also the equations can be rearranged to appear only one of the time derivatives of generalized speeds in each equation. This form is appropriate especially when one intends to derive equations recursively. Hence in addition to the simplicity, the amount of calculations is noticeably reduced and also can be used in a control unit.


1992 ◽  
Vol 07 (11) ◽  
pp. 937-953 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
GAUTAM MANDAL ◽  
SPENTA R. WADIA

We explore consequences of W-infinity symmetry in the fermionic field theory of the c=1 matrix model. We derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a three-dimensional theory and contain non-perturbative information about the model. We use these identities to calculate the two-point function of the bilocal operator in the double scaling limit. We extract the operator whose two-point correlator has a single pole at an (imaginary) integer value of the energy. We then rewrite the W-infinity charges in terms of operators in the matrix model and use this to derive constraints satisfied by the partition function of the matrix model with a general time dependent potential.


Author(s):  
Yan-Qing Ma ◽  
Jian-Wei Qiu

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.


2020 ◽  
pp. 744-788
Author(s):  
Giuseppe Mussardo

At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.


1997 ◽  
Vol 19 (3) ◽  
pp. 59-64
Author(s):  
Do Sanh

In the paper it is given a new form of equations of motion of nonholonomic mechanical systems. The obtained equations are written in a matrix form and in order to establish them it is unnecessary to calculate the inverse matrix of the matrix of inertia. It is important that it is possible to obtain the relation between the error of realizing constraints and that of computing the solution of equations of motion of the system under consideration.


2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Szymon Matuszewski ◽  
Anna Mądra-Bielewicz

AbstractInsects regulate their body temperature mostly behaviourally, by changing posture or microhabitat. Usually they use heat that is already present in the environment. Sometimes, however, they may manipulate the environment to affect, focus or benefit from thermogenesis. Carrion beetles create a feeding matrix by applying to cadaver surface anal or oral exudates. We tested the hypothesis that the matrix, which is formed on carrion by communally breeding beetle Necrodes littoralis L. (Silphidae), produces heat that enhances insect fitness. Using thermal imaging we demonstrate that heat produced in the matrix formed on meat by adult or larval beetles is larger than in meat decomposing without insects. Larval beetles regularly warmed up in the matrix. Moreover, by comparing matrix temperature and larval fitness in colonies with and without preparation of meat by adult beetles, we provide evidence that formation of the matrix by adult beetles has deferred thermal effects for larval microhabitat. We found an increase in heat production of the matrix and a decrease in development time and mortality of larvae after adult beetles applied their exudates on meat in the pre-larval phase. Our findings indicate that spreading of exudates over carrion by Necrodes larvae, apart from other likely functions (e.g. digesting carrion or promoting growth of beneficial microbes), facilitates thermoregulation. In case of adult beetles, this behaviour brings distinct thermal benefits for their offspring and therefore may be viewed as a new form of indirect parental care with an important thermal component.


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