This eBook is devoted to the domain of physics we call Open Quantum Physics, which seemed important for the new field of research of the environmental heat conversion into usable energy. For this research, a special mathematical tool has been used, consisting of master equations for systems of particles as Fermions, Bosons, and electromagnetic field. This effort was based on the previous results of Lindblad, Sandulescu, and Scutaru for a description of the dissipative coupling of a system of interest in accordance with the quantum principles. We used the method of Ford, Lewis, and O’Connell for reducing the total dynamics to a master equation for a system of interest. The results of our research are presented in this eBook in a more general framework of open physics.
This eBook is devoted to the domain of physics we call Open Quantum Physics, which seemed important for the new field of research of the environmental heat conversion into usable energy. For this research, a special mathematical tool has been used, consisting of master equations for systems of particles as Fermions, Bosons, and electromagnetic field. This effort was based on the previous results of Lindblad, Sandulescu, and Scutaru for a description of the dissipative coupling of a system of interest in accordance with the quantum principles. We used the method of Ford, Lewis, and O’Connell for reducing the total dynamics to a master equation for a system of interest. The results of our research are presented in this eBook in a more general framework of open physics.
A Quantum system can be viewed as a larger closed system comprising of two components: an open quantum system and its surrounding environment. These two components interact with each other, and in the realm of theoretical physics, this interaction cannot be neglected. This eBook A Quantum system can be viewed as a larger closed system comprising of two components: an open quantum system and its surrounding environment. These two components interact with each other, and in the realm of theoretical physics, this interaction cannot be neglected. This eBook explains mathematical and statistical co
This text is a short introduction to the physics of driven-dissipative many-body systems, focusing on a few selected topics. Beyond its more ``historical'' interest in the study of atomic physics and quantum optics, presently the modeling and studying dissipative phenomena in open quantum systems is pivotal to understanding quantum hardware platforms. While the lack of a thermodynamic potential for these out-of-equilibrium open systems makes it theoretically challenging to investigate their physics, at the same time it allows going beyond the thermodynamic paradigms and investigating new and exotic phenomena. We will focus on one of the simplest, yet most effective, descriptions of open quantum systems, namely the (Gorini-Kossakowski-Sudarshan-) Lindblad master equation. This phenomenological approach describes quantum systems that weakly interact with their surrounding environment. Although many of the results derived below will apply to any quantum system, we will focus in particular on bosonic/spin systems.
This text is a short introduction to the physics of driven-dissipative many-body systems, focusing on a few selected topics. Beyond its more historical interest in the study of atomic physics and quantum optics, presently the modeling and studying of dissipative phenomena in open quantum systems are pivotal to understanding quantum hardware platforms. Although the lack of a thermodynamic potential for these out-of-equilibrium open systems makes it theoretically challenging to investigate their physics, at the same time it allows one to go beyond the thermodynamic paradigms and investigate new and exotic phenomena. We will focus on one of the simplest, yet most effective, descrip-tions of open quantum systems, namely the (Gorini-Kossakowski-Sudarshan-) Lindblad master equation. This phenomenological approach has been devel-oped to describe quantum systems that weakly interact (Born approximation) with a memoryless (Markovian) surrounding environment. However, it is often a remarkably simple and predictive tool to characterize the essential features of an open quantum system. Although many of the results derived below will ap-ply to any quantum system, we will focus in particular on bosonic/spin systems.
Open quantum systems have drawn attention over decades due to its applicability in the foundation of theoretical physics, e.g. statistical mechanics, quantum mechanics and condensed matter physics. The dynamics of open quantum systems has been described as separate entities from their surrounding environment that consists of a very large number of modes, somehow coupled to the mode of the system. Even though the exact solution of the dynamical behavior of the system is impossible to calculate, we obtain a tentative solution using the crucial Markov approximation. The input-output formalism of the quantum Langevin equation (QLE) has been considered as a useful tool which provides a semi-classical description of the dynamics of the system, whereas the master equation provides a complete picture of the dynamics of the system expressed in terms of density matrix. While studying the dynamics of nonlinear system/environment coupling using QLE, we see, for a small value of external field, that the steady state system field does not change much from the steady state field obtained in the absence of nonlinear dissipation. However, in a case where a stronger external field is applied, we see that the deviation becomes substantial from the solution of linear system. We also see that the nonlinear coupling introduces significant difference in the cavity fluctuation spectrum. The description, therefore, provides a potential explanation of parametric effects in terms of nonlinear dissipation phenomena associated with the nonlinear coupling. Even though the theories developed in the context of open quantum systems have proven to be powerful tools, they do not provide a satisfactory platform to be implemented on non-linear Hamiltonians. We often approximate it by linearizing over nonlinear steady state field amplitude, and therefore, the interesting effects are often overlooked. The limitation of the analytics provokes us to simulate open quantum dynamics numerically. The numerical method consists of transformation of the environmental degrees of freedom to a one-dimensional many-body chain, and the computational technique includes numerical diagonalization and renormalization process. The time-adaptive density matrix renormalisation group (t-DMRG) is known as one of the most powerful techniques for the simulation of strongly-correlated many-body quantum systems. In this thesis, along with the theoretical modeling, we implement DMRG numerical scheme for the simulation of canonical S/B model by mapping it to one-dimensional harmonic chain with nearest neighbor interactions, and use the method to investigate the dynamics of the free dissipative system. The thermalization of open quantum systems is also studied by generating minimally entangled typical thermal states (METTS) through imaginary time evolution, and real-time evolving an empty system in the presence of the thermal bath. Further, we simulate coherently driven free dissipative Kerr nonlinear system numerically using Euler's method by solving Heisenberg equation of motion and t-DMRG algorithm, and demonstrate how the numerical results are analogous to classical bistability. By comparing with analytics, we see that the DMRG numerics is analogous to the quantum-mechanical exact solution obtained by mapping the equation of motion of the density matrix of the system to a Fokker-Plank equation. The comparison between two different numerical techniques shows that the semi-classical Euler's method determines the dynamics of the system field of one among two coherent branches, whereas DMRG numerics gives the superposition of both of them. Hence, DMRG-determined time dynamics undergoes generating non-classical states. Our approach of dealing with nonlinearity represents an important contribution in the developments of technique to study the dynamical and steady-state behavior of open quantum systems, which is a fundamental aspect of quantum physics.
Open quantum systems describe quantum systems that interact unavoidably with their environments. These notes introduce the physical origins of decoherence and dissipation in realistic settings, developing the theoretical framework of reduced dynamics and quantum master equations within the connection to thermodynamics in the quantum regime. Additionally, a set of relevant exercises are proposed to reinforce the acquisition of knowledge. The text equips readers with the tools to model and analyze open quantum dynamics.
This chapter is devoted to Lindblad master equation, obtained by a generalization of the quantum dynamic group to a time dependent semigroup. For this equation, we present a demonstration of Alicki and Lendi, obtained by a linear approximation of the openness operator, which describes the time evolution of a system of interest in an environment. We re-obtain this equation by taking the total dynamic equation with a bilinear dissipative potential in system and environment operators, and tracing over the environment states. In this way, we get physical expressions of the dissipation coefficients, as functions of the system operators. We present the quantum theory of Sandulescu and Scutaru, where the dissipative dynamics is described by friction and diffusion processes, with coefficients which satisfy fundamental constraints.