1
|
Liu F. Semi-Markov processes in open quantum systems. II. Counting statistics with resetting. Phys Rev E 2023; 108:064101. [PMID: 38243423 DOI: 10.1103/physreve.108.064101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 11/09/2023] [Indexed: 01/21/2024]
Abstract
A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump trajectories are no longer semi-Markov. However, focusing on trajectories and using simple probability formulas, general counting statistics can still be constructed from reset-free statistics. An exact tilted matrix equation is also obtained. The inputs of these methods are the survival distributions and waiting-time density distributions instead of quantum operators. In addition, a continuous-time cloning algorithm is introduced to simulate the large-deviation properties of open quantum systems. Several quantum optics systems are used to demonstrate these results.
Collapse
Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100083, China
| |
Collapse
|
2
|
Liu F. Asymptotic large deviations of counting statistics in open quantum systems. Phys Rev E 2023; 108:064111. [PMID: 38243480 DOI: 10.1103/physreve.108.064111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2023] [Accepted: 11/14/2023] [Indexed: 01/21/2024]
Abstract
We use a semi-Markov process method to calculate large deviations of counting statistics for three open quantum systems, including a resonant two-level system and resonant three-level systems in the Λ and V configurations. In the first two systems, radical solutions to the scaled cumulant generating functions are obtained. Although this is impossible in the third system, since a general sixth-degree polynomial equation is present, we still obtain asymptotically large deviations of the complex system. Our results show that, in these open quantum systems, the large deviation rate functions at zero current are equal to two times the largest nonzero real parts of the eigenvalues of operator -iH[over ̂], where H[over ̂] is a non-Hermitian Hamiltonian, while at a large current these functions possess a unified formula.
Collapse
Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
| |
Collapse
|
3
|
de Paula AL, Pereira E. Establishing non-zero energy currents with the one-way street phenomenon and other symmetry properties in boundary driven spin systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:445601. [PMID: 35995040 DOI: 10.1088/1361-648x/ac8bbe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 08/22/2022] [Indexed: 06/15/2023]
Abstract
The aim of this paper is the investigation of properties of the energy current of usual (frequently found in the literature) boundary driven spin systems. For inhomogeneous Heisenberg (XXZandXXX) spin chains, we numerically compute the steady state, in the absence of an external magnetic field, and confirm the previously shown occurrence of the one-way street phenomenon, precisely, there is a nonzero energy current that preserves its magnitude and direction as we invert the baths at the edges, an effect stronger than the perfect rectification (which means current in a direction and zero current as we invert the baths). The consideration of several different polarizations at the edges reestablishes that it is a ubiquitous phenomenon. And, even for these inhomogeneous versions of spin chains, we also establish, by analytical methods, other symmetry properties of the energy current and confirm them by numerical computations.
Collapse
Affiliation(s)
- Alberto L de Paula
- Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais, C. P. 169, Ribeirão das Neves 33858-480, MG, Brazil
| | - Emmanuel Pereira
- Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, Belo Horizonte 30123-970, MG, Brazil
| |
Collapse
|
4
|
Krajnik Ž, Ilievski E, Prosen T. Absence of Normal Fluctuations in an Integrable Magnet. PHYSICAL REVIEW LETTERS 2022; 128:090604. [PMID: 35302808 DOI: 10.1103/physrevlett.128.090604] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Revised: 12/30/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
We investigate dynamical fluctuations of transferred magnetization in the one-dimensional lattice Landau-Lifshitz magnet with uniaxial anisotropy, representing an emblematic model of interacting spins. We demonstrate that the structure of fluctuations in thermal equilibrium depends radically on the characteristic dynamical scale. In the ballistic regime, typical fluctuations are found to follow a normal distribution and scaled cumulants are finite. In stark contrast, on the diffusive and superdiffusive timescales, relevant, respectively, for the easy-axis and isotropic magnet at vanishing total magnetization, typical fluctuations are no longer Gaussian and, remarkably, scaled cumulants are divergent. The observed anomalous features disappear upon breaking integrability, suggesting that the absence of normal fluctuations is intimately tied to the presence of soliton modes. In a nonequilibrium setting of the isotropic magnet with weakly polarized step-profile initial state we find a slow drift of dynamical exponent from the superdiffusive towards the diffusive value.
Collapse
Affiliation(s)
- Žiga Krajnik
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| |
Collapse
|
5
|
de Paula AL, Pereira E, Drumond RC, Aguiar MCO. Energy current manipulation and reversal of rectification in graded XXZ spin chains. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:175403. [PMID: 31935711 DOI: 10.1088/1361-648x/ab6b8c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e. asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e. if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.
Collapse
Affiliation(s)
- Alberto L de Paula
- Departamento de Física, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, MG, Brazil. Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, C. P. 121, 20270-021, Rio de Janeiro, RJ, Brazil
| | | | | | | |
Collapse
|
6
|
Carollo F, Jack RL, Garrahan JP. Unraveling the Large Deviation Statistics of Markovian Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 122:130605. [PMID: 31012635 DOI: 10.1103/physrevlett.122.130605] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Revised: 03/05/2019] [Indexed: 06/09/2023]
Abstract
We analyze dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a quantum level-2.5 large deviation principle for these systems, which describes the joint fluctuations of time-averaged quantum jump rates and of the time-averaged quantum state for long times. Like its level-2.5 counterpart for classical continuous-time Markov chains (which it contains as a special case), this description is both explicit and complete, as the statistics of arbitrary time-extensive dynamical observables can be obtained by contraction from the explicit level-2.5 rate functional we derive. Our approach uses an unraveled representation of the quantum dynamics which allows these statistics to be obtained by analyzing a classical stochastic process in the space of pure states. For quantum reset processes we show that the unraveled dynamics is semi-Markovian and derive bounds on the asymptotic variance of the number of quantum jumps which generalize classical thermodynamic uncertainty relations. We finish by discussing how our level-2.5 approach can be used to study large deviations of nonlinear functions of the state, such as measures of entanglement.
Collapse
Affiliation(s)
- Federico Carollo
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| |
Collapse
|
7
|
Carollo F, Garrahan JP, Lesanovsky I, Pérez-Espigares C. Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains. Phys Rev E 2017; 96:052118. [PMID: 29347714 DOI: 10.1103/physreve.96.052118] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Indexed: 06/07/2023]
Abstract
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.
Collapse
Affiliation(s)
- Federico Carollo
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Carlos Pérez-Espigares
- School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
8
|
Buča B, Prosen T. Charge and spin current statistics of the open Hubbard model with weak coupling to the environment. Phys Rev E 2017; 95:052141. [PMID: 28618579 DOI: 10.1103/physreve.95.052141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 06/07/2023]
Abstract
Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.
Collapse
Affiliation(s)
- Berislav Buča
- Department of Medical Physics and Biophysics, University of Split School of Medicine, 21000 Split, Croatia
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| |
Collapse
|
9
|
Žnidarič M. Large-deviation statistics of a diffusive quantum spin chain and the additivity principle. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042140. [PMID: 24827225 DOI: 10.1103/physreve.89.042140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 06/03/2023]
Abstract
Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative dephasing. We analytically calculate the exact expression for the second current moment in a system of any length and then numerically demonstrate that in the thermodynamic limit, higher-order cumulants and the large-deviation function can be calculated using the additivity principle or macroscopic hydrodynamic theory. This shows that the additivity principle can also hold in systems that are not purely stochastic, and can in particular be valid in quantum systems. We also show that in large systems, the current fluctuations are the same as in the classical symmetric simple exclusion process.
Collapse
Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| |
Collapse
|