scholarly journals Duality in quantum transport models

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Rouven Frassek ◽  
Cristian Giardinà ◽  
Jorge Kurchan
Keyword(s):  
Quantum Transport ◽  
Dynamic Process ◽  
Exclusion Process ◽  
Classical Case ◽  
Quantum Systems ◽  
Original Model ◽  
Transport Models ◽  
Dynamical Symmetries ◽  
Classical Models ◽  
Duality Approach

We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler one, containing only a few particles and (b) shows that any dynamic process of this kind with generic baths may be mapped onto one with equilibrium baths. We exemplify this through the study of a particular model: the quantum symmetric exclusion process introduced in [1]. As in the classical case, the whole construction becomes intelligible by considering the dynamical symmetries of the problem.

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

2015 ◽  
Vol 25 (09) ◽  
pp. 1663-1763 ◽  
Author(s):  
N. Bellomo ◽  
A. Bellouquid ◽  
Y. Tao ◽  
M. Winkler
Keyword(s):  
Blow Up ◽  
Existence Of Solutions ◽  
Biological Tissues ◽  
Original Model ◽  
Future Research ◽  
Macroscopic Models ◽  
The Third ◽  
Research Activities ◽  
Classical Models ◽  
Chemotaxis Models

This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.

Coupling one-dimensional time-dependent classical and quantum transport models

2002 ◽  
Vol 43 (1) ◽  
pp. 1-24 ◽  
Author(s):  
N. Ben Abdallah ◽  
P. Degond ◽  
I. M. Gamba
Keyword(s):  
Quantum Transport ◽  
Time Dependent ◽  
Transport Models ◽  
One Dimensional

scholarly journals Stationary states of weak coupling limit-type Markov generators and quantum transport models

2020 ◽  
Vol 23 (01) ◽  
pp. 2050003
Author(s):  
A. Hernández-Cervantes ◽  
R. Quezada
Keyword(s):  
Quantum Transport ◽  
Weak Coupling ◽  
Energy Transport ◽  
Transport Model ◽  
Weak Coupling Limit ◽  
Stationary States ◽  
Transport Models ◽  
Markov Generator ◽  
Kraus Operators ◽  
Creation Operators

We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al. (modified AKV’s model) studied first in [J. C. García et al., Entangled and dark stationary states of excitation energy transport models in many-particles systems and photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21(3) (2018), Article ID: 1850018, p. 21, doi:10.1142/S0219025718500182], in terms of generalized annihilation and creation operators.

scholarly journals Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder

2019 ◽  
Vol 3 (4) ◽  
pp. 47 ◽  
Author(s):  
Renat T. Sibatov ◽  
HongGuang Sun
Keyword(s):  
Quantum Transport ◽  
Stable Distribution ◽  
Quantum Wires ◽  
Quantum Systems ◽  
Spatial Distributions ◽  
Wire Length ◽  
One Dimensional ◽  
Fractional Equations ◽  
Weak Scattering ◽  
Conductance Distribution

New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuations of conductance and resistance are calculated for different parameters of spatial distributions. A tempered Lévy stable distribution of spacing between barriers leads to a transition in conductance scaling.

Characterizations of symmetric monotone metrics on the state space of quantum systems

2006 ◽  
Vol 6 (7) ◽  
pp. 597-605
Author(s):  
F. Hansen
Keyword(s):  
State Space ◽  
Quantum System ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Classical Case ◽  
Riemannian Metric ◽  
Quantum Systems ◽  
The State ◽  
Stochastic Mappings

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

Simulations of ultrathin SOI with quantum transport models

2002 ◽  
Author(s):  
E. Lyumkis ◽  
R. Mickevicius ◽  
O. Penzin ◽  
B. Polsky ◽  
K. El Sayed ◽  
...  
Keyword(s):  
Quantum Transport ◽  
Transport Models ◽  
Ultrathin Soi

scholarly journals A Green’s function perspective on the nonequilibrium thermodynamics of open quantum systems strongly coupled to baths

2021 ◽  
Author(s):  
Nicolas Bergmann ◽  
Michael Galperin
Keyword(s):  
Green’S Function ◽  
Quantum Transport ◽  
Green's Function ◽  
Nonequilibrium Thermodynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Thermodynamic Consideration ◽  
Strongly Coupled ◽  
Open Quantum ◽  
Weakly Coupled

AbstractWe give a nonequilibrium Green’s function (NEGF) perspective on thermodynamics formulations for open quantum systems that are strongly coupled to baths. A scattering approach implying thermodynamic consideration of a supersystem (system plus baths) that is weakly coupled to external superbaths is compared with the consideration of thermodynamics of a system that is strongly coupled to its baths. We analyze both approaches from the NEGF perspective and argue that the latter yields a possibility of thermodynamic formulation consistent with a dynamical (quantum transport) description.

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