# Alexander E. TeretenkovRussian Academy of Sciences | RAS · Department of Mathematical Methods for Quantum Technologies

Alexander E. Teretenkov

PhD

## About

51

Publications

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313

Citations

Citations since 2016

Introduction

## Publications

Publications (51)

Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in this paper, we derive a model of dissipative time evolution based on unitary Lindblad operators which, while i...

After a short outline of the notion of canonical quantum decomposition of a classical random field and of its connection with the program of non–linear quantization, we concentrate our attention on quadratic quantization. We introduce the \(*\)–Lie algebra of homogeneous quadratic Boson fields denoted \(\hbox {heis}_{2,d}(\mathbb {C})\). Then we re...

We introduce the effective Gibbs state for the observables averaged with respect to fast free dynamics. We prove that the information loss due to the restriction of our measurement capabilities to such averaged observables is non-negative and discuss a thermodynamic role of it. We show that there are a lot of similarities between this effective Ham...

In this paper, we discuss effective quantum dynamics obtained by averaging projector with respect to free dynamics. For unitary dynamics generated by quadratic fermionic Hamiltonians, we obtain effective Heisenberg dynamics. By perturbative expansions, we obtain the correspondent effective time-local Heisenberg equations. We also discuss a similar...

We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and obtain their solutions. Based on them we also derive similar equations for the case of the quantum master equation,...

The explicit dynamics of the moments for the GKSL equation and the approach in finding stationary Gaussian states are obtained. In our case the GKSL equation corresponds to Wiener stochastic processes. Such equations contain a double commutator which can be understood as a quantum analog of the second spatial derivative.

We discuss effective quantum dynamics obtained by averaging projector with respect to free dynamics. For unitary dynamics generated by quadratic fermionic Hamiltonians we obtain effective Heisenberg dynamics. By perturbative expansions we obtain the correspondent effective time-local Heisenberg equations. We also discuss a similar problem for boson...

We obtain an algorithm for the skew-Takagi factorization based on the singular value decomposition. As an example application of such an algorithm, we consider the computation of Heisenberg evolution of the fermionic creation and annihilation operators in the case of the quadratic Hamiltonian of a special form

We consider the effective Gibbs state for averaged observables. In particular, we perturbatively calculate the correspondent effective Hamiltonian. We show that there are a lot of similarities between this effective Hamiltonian and the mean force Hamiltonian. We also discuss a thermodynamic role of the information loss due to restriction of our mea...

For the model of a multi-level system in the rotating wave approximation we obtain the corrections for a usual weak coupling limit dynamics by means of perturbation theory with Bogolubov-van Hove scaling. It generalizes our previous results on a spin-boson model in the rotating wave approximation. Additionally, in this work we take into account som...

Рассмотрен простой пример вполне положительной динамики, для которого как генератор нелокального интегро-дифференциального уравнения, приводящего к такой динамике, так и локальный по времени генератор могут быть вычислены явно. Продемонстрирована возможность воспроизвести на этом простом примере при соответствующем вводе в него малого параметра нек...

Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in this article, we derive a new model of dissipative time evolution based on unitary Lindblad operators which, w...

For the model of a multi-level system in the rotating wave approximation we obtain the corrections for a usual weak coupling limit dynamics by means of perturbation theory with Bogolubov-van Hove scaling. It generalizes our previous results on a spin-boson model in the rotating wave approximation. Additionally, in this work we take into account som...

We study the perturbation expansion near the Bogolubov-van Hove limit, where a small parameter is introduced both in the coupling constant and in the time. We show that such a perturbation theory is singular. In particular, we show that the initial condition for the perturbative part of the density matrix differs from the one for the whole density...

We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we decompose a matrix as a skew-Hamiltonian and a symplectic matrix. We apply our results to study bosonic Gaussian cha...

Gorini-Kossakowski-Sudarshan-Lindblad equation of Poisson-type for the density matrix is considered. The Poisson jumps are assumed to be unitary operators with generators, which are quadratic in fermionic creation and annihilation operators. The explicit dynamics of the density matrix moments and Markovian multi-time ordered correlation functions i...

We introduce the Friedrichs model at finite temperature which is one- and zero-particle restriction of spin-boson in the rotating wave approximation and obtain the population of the excited state for this model. We also consider the oscillator interacting with bosonic thermal bath in the rotating wave approximation and obtain dynamics of mean excit...

The model of a multi-level system interacting with several reservoirs is considered. The exact reduced density matrix evolution could be obtained for this model without Markov approximation. Namely, this evolution is fully defined by the finite set of linear differential equations. In this work the results which were obtained previously for only on...

We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.

Both quantum information features and irreversible quantum evolution of the models arising in physical systems in one-particle approximation are discussed. It is shown that the calculation of the reduced density matrix and entanglement analysis are considerably simplified in this case. The irreversible quantum evolution described by Gorini--Kossako...

We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.

An exactly solvable model for the multi-level system interacting with several reservoirs at zero temperatures is presented. Population decay rates and decoherence rates predicted by exact solution and several approximate master equations, which are widespread in physical literature, are compared. The space of parameters is classified with respect t...

The explicit dynamics of the moments for the GKSL equation is obtained. In our case the GKSL equation corresponds to Poisson stochastic processes which lead to unitary jumps. We consider squeeze operators as the unitary jumps.

We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we decompose a matrix as a skew-Hamiltonian and a symplectic matrix. We apply our results to study bosonic Gaussian cha...

В работе излагается метод псевдомод, при этом особый акцент сделан на формулировке данного метода в терминах уравнений Горини-Коссаковского-Сударшана-Линдблада. Показывается связь метода псевдомод с решением модели Фридрихса, а также модели Джейнса-Каммингса с диссипацией при нулевой температуре. Полученные результаты применяются для описания немар...

The pseudomode approach is discussed, with emphasis on the Gorini-Kossakowski-Sudarshan-Lindblad form of this approach. The connection of the pseudomode approach with solutions of the Friedrichs model and the Jaynes-Cummings model with dissipation at zero temperature is shown. The obtained results are applied to the description of non-Markovian phe...

An exactly solvable model for the multi-level system interacting with several reservoirs at zero temperatures is presented. Population decay rates and decoherence rates predicted by exact solution and several approximate master equations, which are widespread in physical literature, are compared. The space of parameters is classified with respect t...

The pseudomode approach is discussed with an emphasis to Gorini-Kossakowski-Sudarshan-Lindblad form of this approach. The connection of the pseudomode approach with solutions of both the Friedrichs model and Jaynes-Cummings model with dissipation at zero temperature is shown. The obtained results are applied to non-Markovian phenomena description i...

Gaussian solutions of the Cauchy problem for the GKS-L equation (in the Schrödinger picture) with quadratic fermionic generators are obtained. These Gaussian solutions are represented both as exponentials of quadratic forms in fermionic creation-annihilation operators and by their normal symbols. The coefficients of these forms are represented as a...

The solution of the Cauchy problem for the Gorini–Kossakowski–Sudarshan–Lindblad equation describing the irreversible quantum evolution of an n-particle system with a generator, which is a quadratic function in creation-annihilation operators, is reduced to the calculation of standard algebraic functions of 2n × 2n matrices.

A three-level quantum system interacting with non-equilibrium environment is investigated. The stationary state of the system is found (both for non-coherent and coherent environment) and relaxation and decoherence to the stationary state is described. The stationary state of the system will be non-equilibrium and will generate flows. We describe t...

We describe a simple implementation of the Takagi factorization of symmetric matrices A=UΛUTA=UΛUT with unitary U and diagonal Λ≥0Λ≥0 in terms of the square root of an auxiliary unitary matrix and the singular value decomposition of A. The method is based on an algebraically exact expression.
For parameterized family Aε=A+εR=UεΛεUεT, ε≥0ε≥0 with di...