Theoretical and Numerical Studies of the Dynamics of Open Quantum 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
inputoutput formalism of the quantum Langevin equation (QLE) has been considered
as a useful tool which provides a semiclassical 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 nonlinear 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 onedimensional manybody chain, and the computational
technique includes numerical diagonalization and renormalization process.
The timeadaptive density matrix renormalisation group (tDMRG) is known as one
of the most powerful techniques for the simulation of stronglycorrelated manybody
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 onedimensional 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 realtime 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 tDMRG 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 quantummechanical
exact solution obtained by mapping the equation of motion of the density matrix of
the system to a FokkerPlank equation. The comparison between two different numerical
techniques shows that the semiclassical 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, DMRGdetermined time dynamics
undergoes generating nonclassical states. Our approach of dealing with nonlinearity
represents an important contribution in the developments of technique to study the
dynamical and steadystate behavior of open quantum systems, which is a fundamental
aspect of quantum physics.
...
ISBN
9789513981495Contains publications
 Artikkeli I: Manninen, Juuso; Agasti, Souvik; Massel, Francesco (2017). Nonlinear quantum Langevin equations for bosonic modes in solidstate systems. Physical Review A, 96 (6), 063830. DOI: 10.1103/PhysRevA.96.063830
 Artikkeli I: Agasti, Souvik (2019). Numerical simulation of Kerr nonlinear systems : analyzing nonclassical dynamics. Journal of Physics Communications, 3 (10), 105004. DOI: 10.1088/23996528/ab4690
 Artikkeli III: Agasti, Souvik (2020). Simulation of Matrix Product States For Dissipation and Thermalization Dynamics of Open Quantum Systems. Journal of Physics Communications, 4 (1), 015002. DOI: 10.1088/23996528/ab6141
 Artikkeli IV: Agasti, Souvik (2020). Numerical simulation of free dissipative open quantum system and establishment of a formula for π. In Shekhawat, Manoj Singh; Bhardwaj, Sudhir; Suthar, Bhuvneshwer (Eds.) ICC2019 : 3rd International Conference on Condensed Matter and Applied Physics, AIP Conference Proceedings, 2220. American Institute of Physics, 130010. DOI: 10.1063/5.0001282. JYX: jyx.jyu.fi/handle/123456789/68859.
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