Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath

Еремин, В. В.; Glebov, I. O.

doi:10.1007/s11232-007-0128-7

Cited by 6 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper continues previous papers aimed at analytically describing the dissipative dynamics in the harmonic approximation [12]. In [13], we obtained closed expressions for the Redfield tensor elements, which allowed finding the explicit time dependence of the mean oscillation energy. Here, we generalize this result to a whole class of operators for which we find the exponential temporal damping of means and find the corresponding relaxation times.…”

Section: Introductionsupporting

confidence: 62%

“…The total Hamiltonian is the sum of terms corresponding to the observed system H S , the heat bath H B , and their interaction V. The interaction operator is taken to be linear in both the oscillator and the heat bath coordinates [13]:…”

Section: The Modelmentioning

confidence: 99%

“…This follows from the realness of the diagonal elements of the density matrix and from the existence of the limit values σ ii (∞) [13]. Performing a linear transformation of the diagonal elements σ ii (t), we can pass to the one-exponential dependence for each of the numbers k j :…”

Section: The Modelmentioning

confidence: 99%

See 2 more Smart Citations

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

Glebov

Еремин

2010

Theor Math Phys

Self Cite

View full text Add to dashboard Cite

We consider the problem of the dissipative dynamics of a harmonic oscillator linearly coupled to a heat bath. We demonstrate that in addition to the mean energy, there exists an infinite series of quantities exponentially decreasing in time that are means of polynomials of the system Hamiltonian. We obtain the spectrum of the corresponding relaxation times. We propose a method for representing the time characteristics of the system in terms of operators corresponding to the exponentially damped observables. We obtain a recurrence relation for these operators.

show abstract

Section: Introductionsupporting

confidence: 62%

Section: The Modelmentioning

confidence: 99%

See 1 more Smart Citation

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

Glebov

Еремин

2010

Theor Math Phys

Self Cite

View full text Add to dashboard Cite

show abstract

“…This approach can be used in many problems that admit simple approximations (the harmonic approximation for describing the vibrational system states, a bilinear form of the system-bath interaction, etc.) and analytically solvable problems [15]. We also note that in modeling macromolecular system dynamics, we can always subdivide it into systems that admit simple approximations.…”

Section: Resultsmentioning

confidence: 99%

“…Correlation matrices (15) and (19) coincide, and matrices (17) and (18) are obtained by transposition and changing the sign of the time.…”

Section: The Correlation Function Matrixmentioning

confidence: 99%

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

Glebov

Еремин

2009

Theor Math Phys

Self Cite

View full text Add to dashboard Cite

In the Redfield theory framework, we consider the problem of the vibrational dynamics in dissipative systems. We decompose the Hamiltonian of interaction of the observed system with a thermal bath into terms that are products of system transition operators and bath transition operators. Using the decomposition, we construct a correlation function matrix containing all the information about the interaction of the system with the bath and obtain a new operator form of the Redfield equation. We consider the procedure for factoring the interaction operator and constructing the correlation function matrix. Using the diagonalization of the obtained matrix, we give correlated dissipation operators, whose introduction simplifies the form of the Redfield equations. We show that for several problems in which fundamental transition frequencies can be chosen, this procedure significantly reduces the dimensionality of the dissipative dynamics problem.

show abstract

Transient structures and chemical reaction dynamics

Ischenko¹,

Weber²,

Miller³

2017

Russ. Chem. Rev.

View full text Add to dashboard Cite

To study transition structures that are formed in real time during a chemical reaction process, it is necessary to use ultrafast methods to follow the structural dynamics of molecular systems. For many decades, optical methods have been used to study the electronic states and time course giving rise to structural intermediates of chemical reactions with an ever higher time resolution. Although in some cases optical methods show many details, ultimately the results of these observations give only indirect information about the structure of the chemical reaction intermediates. Experimental observation of the behaviour of matter in the space-time continuum on ultrashort time scale is the necessary first step to explain and, subsequently, to control the nonequilibrium processes and functionality of the systems under study, to trace the relationship between the elements of the triad 'Structure–Dynamics–Function' to fully understand material properties. The results of these studies provide the necessary new information for testing theoretical approaches to the description of nonequilibrium chemical dynamics of molecular systems. The study of the time sequence of ultrafast processes occurring during the evolution of intermediate structures in the course of chemical reactions requires the integration of information that can be obtained by using complementary diffraction and spectroscopic methods based on various physical phenomena. Integration of data from ultrafast diffraction and spectroscopy makes it possible to investigate timescales prior to the onset of dissipation in which the coherent dynamics of matter can be observed. The use of quantum chemical calculations has reached a level of sophistication that makes it possible to explain the results of these experimental studies, the features of nonadiabatic behaviour of intermediate structures, and transition states of chemical reactions of molecular systems. This review analyzes the achievements of this rapidly developing field of modern chemistry, femtochemistry, to observe the primary events directing chemistry. The bibliography includes 580 references

show abstract

Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath

Cited by 6 publications

References 16 publications

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

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

Transient structures and chemical reaction dynamics

Contact Info

Product

Resources

About