scholarly journals Klein's programme and quantum mechanics

2015 ◽  
Vol 12 (06) ◽  
pp. 1560006
Author(s):  
Jesús Clemente-Gallardo ◽  
Giuseppe Marmo
Keyword(s):  
Quantum Mechanics ◽  
Linear Group ◽  
Unitary Group ◽  
General Linear Group ◽  
Open Quantum Systems ◽  
Compact Subgroup ◽  
Quantum Systems ◽  
General Linear ◽  
C Algebra ◽  
Open Quantum

We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.

scholarly journals Adiabatic theorems for general linear operators with time-independent domains

2019 ◽  
Vol 31 (05) ◽  
pp. 1950014 ◽  
Author(s):  
Jochen Schmid
Keyword(s):  
Banach Space ◽  
Spectral Gap ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Linear Operators ◽  
General Linear ◽  
Regularity Conditions ◽  
Time Varying ◽  
Open Quantum ◽  
Adiabatic Switching

We establish adiabatic theorems with and without spectral gap conditions for general — typically dissipative — linear operators [Formula: see text] with time-independent domains [Formula: see text] in some Banach space [Formula: see text]. Compared to the previously known adiabatic theorems — especially those without a spectral gap condition — we do not require the considered spectral values [Formula: see text] of [Formula: see text] to be (weakly) semisimple. We also impose only fairly weak regularity conditions. Applications are given to slowly time-varying open quantum systems and to adiabatic switching processes.

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Hamiltonian assignment for open quantum systems

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Eugene F. Dumitrescu ◽  
Pavel Lougovski
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

Sign in / Sign up

Export Citation Format

Share Document