scholarly journals NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS

2013 ◽  
Vol 27 (27) ◽  
pp. 1350163 ◽  
Author(s):  
ALESSANDRO SERGI ◽  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
Time Evolution ◽  
Density Operator ◽  
Quantum Dynamics ◽  
Population Difference ◽  
Level System ◽  
Different Types ◽  
Dissipative Environments ◽  
Dissipative Environment

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system (TLS) coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling TLS. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing, vanishing population difference and purification.

The Quantum Mechanical Density Operator And Its Time Evolution: Quantum Dynamics Using The Quantum Liouville Equation

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Phase Space ◽  
Probability Density ◽  
Time Evolution ◽  
Liouville Equation ◽  
Density Operator ◽  
Quantum Dynamics ◽  
Quantum Mechanical ◽  
Initial Condition ◽  
Initial State ◽  
Thermal Environments

The starting point of the classical description of motion is the Newton equations that yield a phase space trajectory (rN (t), pN (t)) for a given initial condition (rN (0), pN (0)). Alternatively one may describe classical motion in the framework of the Liouville equation (Section (1.2.2)) that describes the time evolution of the phase space probability density f (rN , pN ; t). For a closed system fully described in terms of a well specified initial condition, the two descriptions are completely equivalent. Probabilistic treatment becomes essential in reduced descriptions that focus on parts of an overall system, as was demonstrated in Sections 5.1–5.3 for equilibrium systems, and in Chapters 7 and 8 that focus on the time evolution of classical systems that interact with their thermal environments. This chapter deals with the analogous quantum mechanical problem. Within the limitations imposed by its nature as expressed, for example, by Heisenbergtype uncertainty principles, the Schrödinger equation is deterministic. Obviously it describes a deterministic evolution of the quantum mechanical wavefunction. The analog of the phase space probability density f (rN , pN ; t) is now the quantum mechanical density operator (often referred to as the “density matrix”), whose time evolution is determined by the quantum Liouville equation. Again, when the system is fully described in terms of a well specified initial wavefunction, the two descriptions are equivalent. The density operator formalism can, however, be carried over to situations where the initial state of the system is not well characterized and/or a reduced description of part of the overall system is desired. Such situations are considered later in this chapter.

scholarly journals Optimal entanglement generation in cavity QED with dissipation

2009 ◽  
Vol 87 (9) ◽  
pp. 1031-1036 ◽  
Author(s):  
Jian-Song Zhang ◽  
Jing-Bo Xu
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Cavity Qed ◽  
Density Operator ◽  
Interaction Time ◽  
Entanglement Generation ◽  
Driving Field ◽  
Level Atom ◽  
Field Environment ◽  
Dissipative Environment

We investigate a two-level atom coupled to a cavity with a strong classical driving field in a dissipative environment and find an analytical expression for the time evolution density matrix for the system. The analytical density operator is then used to study the entanglement between the atom and cavity by considering the competing process between the atom–field interactions and the field–environment interactions. It is shown that there is an optimal interaction time for generating atom–cavity entanglement.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

scholarly journals DISSIPATIVE QUANTUM DISORDERED MODELS

2006 ◽  
Vol 20 (19) ◽  
pp. 2795-2804 ◽  
Author(s):  
LETICIA F. CUGLIANDOLO
Keyword(s):  
Glassy Phase ◽  
Quantum Critical Point ◽  
Mean Field ◽  
Static Properties ◽  
One Dimensional ◽  
Time Dynamics ◽  
Long Range Interactions ◽  
Disordered Models ◽  
Different Types ◽  
Dissipative Environments

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered – glassy – phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random king chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.

scholarly journals Hidden Nambu mechanics II: Quantum/semiclassical dynamics

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Atsushi Horikoshi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Extended Phase ◽  
Nambu Mechanics ◽  
Mechanical Structure ◽  
Wave Packet Dynamics ◽  
Semiclassical Dynamics ◽  
Metastable Potential

Abstract Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, including composite operators, can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator, and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems; however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism we present two sets of numerical results on semiclassical dynamics: from a one-dimensional metastable potential model and a simplified Henon–Heiles model of two interacting oscillators.

scholarly journals Exactly thermalized quantum dynamics of the spin-boson model coupled to a dissipative environment

2020 ◽  
Vol 101 (22) ◽  
Author(s):  
M. A. Lane ◽  
D. Matos ◽  
I. J. Ford ◽  
L. Kantorovich
Keyword(s):  
Quantum Dynamics ◽  
Boson Model ◽  
Dissipative Environment

scholarly journals Regional and inter-regional effects in evolving climate networks

2014 ◽  
Vol 21 (2) ◽  
pp. 451-462 ◽  
Author(s):  
J. Hlinka ◽  
D. Hartman ◽  
N. Jajcay ◽  
M. Vejmelka ◽  
R. Donner ◽  
...  
Keyword(s):  
Time Evolution ◽  
El Niño ◽  
El Nino ◽  
Principal Component ◽  
Graph Models ◽  
Network Nodes ◽  
Network Characteristics ◽  
Evolving Networks ◽  
Regional Effects ◽  
Different Types

Abstract. Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system's behaviour. More detailed graph models may include edge weights, orientations or multiple types of links; potential time-dependency of edges is conveniently captured in so-called evolving networks. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El Niño episodes described in the literature. The time evolution of several graph characteristics has been compared with the intervals of El Niño and La Niña episodes. In this study we identify the sources of the evolving network characteristics by considering a reduced-dimensionality description of the climate system using network nodes given by rotated principal component analysis. The time evolution of structures in local intra-component networks is studied and compared to evolving inter-component connectivity.

scholarly journals Observation and quantification of the quantum dynamics of a strong-field excited multi-level system

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Zuoye Liu ◽  
Quanjun Wang ◽  
Jingjie Ding ◽  
Stefano M. Cavaletto ◽  
Thomas Pfeifer ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Strong Field ◽  
Level System ◽  
Multi Level

FIELD PURIFICATION OF A GENERAL THREE-LEVEL SYSTEM INTERACTING WITH RADIATION

2003 ◽  
Vol 17 (07) ◽  
pp. 253-262 ◽  
Author(s):  
MAHMOUD ABDEL-ATY
Keyword(s):  
Exact Solution ◽  
Electromagnetic Field ◽  
Density Operator ◽  
Photon Number ◽  
Entangled State ◽  
Level System ◽  
Level Atom ◽  
Coherent Field ◽  
Field Purity ◽  
Intensity Dependent Coupling

In this essay we introduce a new Hamiltonian which represents the interaction between a three-level atom and a single electromagnetic field including arbitrary forms of nonlinearities of both the field and the intensity-dependent coupling. We derive an exact solution for the density operator of the system by means of which we study the field purity for the entangled state of the system. Also, the influences of the nonlinearities on the field purity and mean photon number are examined. Under the condition of an initial coherent field, the field purity shows the collapse-revival phenomenon. It is found that features of these phenomenon are sensitive to the changes of different kinds of the nonlinearities.

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