ALGEBRAIC CONDITIONS FOR CONVERGENCE OF A QUANTUM MARKOV SEMIGROUP TO A STEADY STATE

Let [Formula: see text] be a uniformly continuous quantum Markov semigroup on [Formula: see text] with generator represented in a standard GKSL form [Formula: see text] and a faithful normal invariant state ρ. In this note we give new algebraic conditions for proving that [Formula: see text] converges towards a steady state, possibly different from ρ. Indeed, we show that this happens whenever the commutator of [Formula: see text] (i.e. its fixed point algebra) coincides with the commutator of [Formula: see text] (where δH(X) = [H, X]) for some n ≥ 1. As an application we discuss the convergence to the unique invariant state of a spin chain model.

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On the range of the generator of a quantum Markov semigroup

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025715500277 ◽

2015 ◽

Vol 18 (04) ◽

pp. 1550027 ◽

Cited By ~ 1

Author(s):

Jorge R. Bolaños-Servin ◽

Franco Fagnola

Keyword(s):

Fixed Point ◽

Infinitesimal Generator ◽

Markov Semigroup ◽

Invariant State ◽

Markov Semigroups ◽

Quantum Markov Semigroup ◽

Kms Condition ◽

Fixed Point Algebra

We show that the commutant of the range of the infinitesimal generator of a norm-continuous quantum Markov semigroup on [Formula: see text], not consisting of identity maps, with a faithful normal invariant state is trivial whenever the fixed point algebra is atomic. As a consequence, two formulations of the irreversible [Formula: see text]-KMS condition proposed in Ref. 2 are equivalent for this class of quantum Markov semigroups.

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THE DECOHERENCE-FREE SUBALGEBRA OF A QUANTUM MARKOV SEMIGROUP WITH UNBOUNDED GENERATOR

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025710004176 ◽

2010 ◽

Vol 13 (03) ◽

pp. 413-433 ◽

Cited By ~ 23

Author(s):

AMEUR DHAHRI ◽

FRANCO FAGNOLA ◽

ROLANDO REBOLLEDO

Keyword(s):

Steady State ◽

Regularity Conditions ◽

Markov Semigroup ◽

Invariant State ◽

Markov Semigroups ◽

Completely Positive Maps ◽

Completely Positive ◽

Infinite Dimensional ◽

Positive Maps ◽

Quantum Markov Semigroup

Let [Formula: see text] be a quantum Markov semigroup on [Formula: see text] with a faithful normal invariant state ρ. The decoherence-free subalgebra [Formula: see text] of [Formula: see text] is the biggest subalgebra of [Formula: see text] where the completely positive maps [Formula: see text] act as homomorphisms. When [Formula: see text] is the minimal semigroup whose generator is represented in a generalised GKSL form [Formula: see text], with possibly unbounded H, Lℓ, we show that [Formula: see text] coincides with the generalised commutator of [Formula: see text] under some natural regularity conditions. As a corollary we derive simple sufficient algebraic conditions for convergence towards a steady state based on multiple commutators of H and Lℓ. We give examples of quantum Markov semigroups [Formula: see text], with h infinite-dimensional, having a non-trivial decoherence-free subalgebra.

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1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

Optical and Quantum Electronics ◽

10.1007/s11082-021-02739-9 ◽

2021 ◽

Vol 53 (2) ◽

Cited By ~ 1

Author(s):

K. Hosseini ◽

L. Kaur ◽

M. Mirzazadeh ◽

H. M. Baskonus

Keyword(s):

Spin Chain ◽

Time Derivative ◽

Soliton Solutions ◽

Chain Model ◽

Heisenberg Ferromagnetic Spin Chain ◽

Spin Chain Model

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SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.11.9 ◽

2021 ◽

Vol 10 (11) ◽

pp. 3491-3504

Author(s):

A. Darwish ◽

H.M. Ahmed ◽

M. Ammar ◽

M.H. Ali ◽

A.H. Arnous

Keyword(s):

Periodic Solutions ◽

Exponential Function ◽

Spin Chain ◽

Function Method ◽

Chain Model ◽

Bright Solitons ◽

Dark Solitons ◽

Heisenberg Ferromagnetic Spin Chain ◽

Spin Chain Model ◽

Chain Equation

This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

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Graded off-diagonal Bethe ansatz solution of the SU(2|2) spin chain model with generic integrable boundaries

Nuclear Physics B ◽

10.1016/j.nuclphysb.2020.115206 ◽

2020 ◽

Vol 960 ◽

pp. 115206

Author(s):

Xiaotian Xu ◽

Junpeng Cao ◽

Yi Qiao ◽

Wen-Li Yang ◽

Kangjie Shi ◽

...

Keyword(s):

Bethe Ansatz ◽

Spin Chain ◽

Chain Model ◽

Spin Chain Model ◽

Bethe Ansatz Solution

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The quantum speed limit time of a two-qubit XYZ spin chain with intrinsic decoherence

Modern Physics Letters A ◽

10.1142/s0217732320502442 ◽

2020 ◽

Vol 35 (29) ◽

pp. 2050244

Author(s):

Lu Hou ◽

Bin Shao ◽

Yuguang Zhu

Keyword(s):

Magnetic Field ◽

Spin Chain ◽

Quantum Correlation ◽

Speed Limit ◽

Chain Model ◽

Intrinsic Decoherence ◽

Physical Reason ◽

Limit Time ◽

Spin Chain Model ◽

Initial States

We study the quantum speed limit (QSL) time of the two-qubit XYZ spin chain model with the influence of intrinsic decoherence. We show that the intrinsic decoherence can suppress the evolution of this system, no matter what initial states the two qubits start from. The investigation of entanglement reveals that quantum correlation is the physical reason for the acceleration of the system. In addition, we also demonstrate that for different initial states, external magnetic field may have opposite influence on QSL time and it mainly derives from the inhibition of entanglement as magnetic field increases.

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Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures

Physical Review A ◽

10.1103/physreva.95.043630 ◽

2017 ◽

Vol 95 (4) ◽

Cited By ~ 18

Author(s):

F. Deuretzbacher ◽

D. Becker ◽

J. Bjerlin ◽

S. M. Reimann ◽

L. Santos

Keyword(s):

Spin Chain ◽

Chain Model ◽

One Dimensional ◽

Strongly Interacting ◽

Spin Chain Model

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The open XXZ spin chain model and the topological basis realization

International Journal of Quantum Information ◽

10.1142/s0219749916500180 ◽

2016 ◽

Vol 14 (03) ◽

pp. 1650018 ◽

Cited By ~ 1

Author(s):

Qingyong Wang ◽

Yangyang Du ◽

Chunfeng Wu ◽

Gangcheng Wang ◽

Chunfang Sun ◽

...

Keyword(s):

Spin Chain ◽

Boundary Term ◽

Chain Model ◽

Topological Parameter ◽

Xxz Chain ◽

Spin Chain Model

In this paper, it is shown that the Hamiltonian of the open spin-1 XXZ chain model can be constructed from the generators of the Birman–Murakami–Wenzl (B–M–W) algebra. Without the topological parameter d (describing the unknotted loop [Formula: see text] in topology) reducing to a fixed value, the topological basis states can be connected with the open XXZ spin chain. Then some particular properties of the topological basis states in this system have been investigated. We find that the topological basis states are the three eigenstates of a four-spin-1 XXZ chain model without boundary term. Specifically, all the spin single states of the system fall on the topological basis subspace. And the number of the spin single states of the system is equal to that of the topological basis states.

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