Theoretical and Numerical Studies of the Dynamics of Open Quantum Systems
Julkaistu sarjassa
JYU dissertationsTekijät
Päivämäärä
2020Tekijänoikeudet
© The Author & University of Jyväskylä
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.
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Julkaisija
Jyväskylän yliopistoISBN
978-951-39-8149-5ISSN Hae Julkaisufoorumista
2489-9003Julkaisuun sisältyy osajulkaisuja
- Artikkeli I: Manninen, Juuso; Agasti, Souvik; Massel, Francesco (2017). Nonlinear quantum Langevin equations for bosonic modes in solid-state 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 non-classical dynamics. Journal of Physics Communications, 3 (10), 105004. DOI: 10.1088/2399-6528/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: 10.1088/2399-6528/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.) ICC-2019 : 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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