Abstract. Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore how to control the quantum state, and also how to bring the state into a target state. Here, we investigate a pure quantum mechanical dynamics, dynamics in quantum Monte Carlo simulation and also in quantum master equation. For the control magnetic states, operators which do not commute with magnetization are important. We study case of the transverse Ising model, in which we compare natures of thermal and quantum fluctuations. We also study the cases of the Dzyaloshinsky-Moriya interaction, where we find a peculiar energy level structure. Moreover we study the case of itinerant magnetic state, where we study the change from the Mott insulator to the Nagaoka ferromagnetic state. Effects of dissipation are also discussed. 1.
Abstract. Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore how to control the quantum state, and also how to bring the state into a target state. Here, we investigate a pure quantum mechanical dynamics, dynamics in quantum Monte Carlo simulation and also in quantum master equation. For the control magnetic states, operators which do not commute with magnetization are important. We study case of the transverse Ising model, in which we compare natures of thermal and quantum fluctuations. We also study the cases of the Dzyaloshinsky-Moriya interaction, where we find a peculiar energy level structure. Moreover we study the case of itinerant magnetic state, where we study the change from the Mott insulator to the Nagaoka ferromagnetic state. Effects of dissipation are also discussed. 1.
Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore how to control the quantum state, and also how to bring the state into a target state. Here, we investigate a pure quantum mechanical dynamics, dynamics in quantum Monte Carlo simulation and also in quantum master equation. For the control magnetic states, operators which do not commute with magnetization are important. We study case of the transverse Ising model, in which we compare natures of thermal and quantum fluctuations. We also study the cases of the Dzyaloshinsky-Moriya interaction, where we find a peculiar energy level structure. Moreover we study the case of itinerant magnetic state, where we study the change from the Mott insulator to the Nagaoka ferromagnetic state. Effects of dissipation are also discussed.
We will discuss on the quantum dynamics on the following three cases. (1) First, we will study structure of adiabatic energy levels for a triangle magnetic cluster with the Dzyaloshinsky-Moriya (DM) interaction. Generally, in single molecular magnets, the magnetic energy levels are discrete and we can find various interesting magnetic behavior when we sweep the external magnetic field. For the dynamics, the adiabatic energy level structure, in particular, avoided level structures at the energy level crossings, plays an important role. The mechanism to open the gap is attributed to some interactions which do not commute with the magnetization. We will discuss dependence of the dynamical magnetization process under the field cycling on the angle between the DM interaction vector and the external magnetic fields.[1,2] We also discuss a hidden conserved quantity due to the chiral symmetry.[3] The dynamical DM effect will be also discussed. (2) We will study the quantum dynamics of one-dimensional transverse Ising model which exhibits a quantum phase transition at zero temperature. There, we find a metastable state and a kind of spinodal decomposition phenomena in the sense of the quantum dynamics. We also refer to the cases of very fast sweep where some size independent collective motions are observed.[4] (3) Finally, we will also study an itinerant electron system in which the Mott insulator-Nagaoka ferromagnetism transition. There, we study the adiabatic change from the Mott insulator to the Nagaoka ferromagnetic state under removal of an electron from the lattice. We also study the magnetization process as a function of the magnetic field.
The theory of open quantum systems represents one of the major developments of quantum mechanics over the last 50 years. Its central object of study is constituted by quantum systems that cannot be regarded as fully isolated, but instead interact with additional degrees of freedom, giving rise to irreversible phenomena such as dissipation and decoherence. The tools provided by this framework are nowadays of paramount importance across many active areas of research, including quantum computation, thermodynamics, metrology and biology. In this thesis, we investigate three main topics within the field. The first contribution concerns the microscopic derivation of the evolution equations, socalled quantum master equations, for open systems which are also subject to external driving fields. Standard techniques developed for time-independent Hamiltonians encounter several difficulties in the time-dependent case, largely restricting their applicability to specific instances, such as periodic or adiabatic drivings. In contrast, a core result of the derivation presented in the thesis is that, when the environment is sufficiently Markovian (essentially, memoryless), the non-adiabatic contributions to the driving field can be neglected in a controlled fashion, yielding an accurate master equation with time-dependent generator, capable of correctly reproducing the open dynamics even for strong drivings. This result is further supported by benchmarks against numerically exact simulations. The second contribution addresses the long-time behavior of general types of (Markovian) quantum master equations, including those of the form introduced above. While this problem has been extensively analyzed in the time-independent setting, virtually no results are known for time-dependent generators. In particular, we establish the foundations of a general theory of relaxation, that is, convergence towards an asymptotic trajectory in the long-time limit, independently of the initial state. The main results include a theorem guaranteeing sufficient conditions for relaxation and the derivation of a rate function governing the convergence to the asymptotic trajectory. The analysis is further extended to a simple non-Markovian case. Moreover, we treat in detail the specific master equation derived in the first part, connecting the aforementioned relaxation property directly to the underlying microscopic dynamics. The third contribution investigates chirality-induced spin selectivity (CISS) effects from the perspective of open quantum systems. Although the majority of theoretical studies aiming to model CISS are based on a coherent description of the spin dynamics, such effects have been observed also for electrons subject to incoherent transport across molecular networks. In this regard, we provide a rigorous ab initio derivation of the microscopic Hamiltonian describing the electronic transport, incorporating electron spin effects and contributions stemming from the nuclear vibrations. Within this result, we critically revise a master equation approach aiming to explain the origin of CISS effects observed in photosynthetic complexes. Taken together, these contributions offer fresh insights and original results on the interplay between driving fields and dissipation, relaxation phenomena, and electronic spin transport in the presence of incoherent dynamics. More broadly, these results provide new theoretical tools with several potential applications in quantum technologies, from modeling of control pulses in noisy environments to quantum reservoir engineering, and contribute to a deeper understanding of the role of quantum effects in biological systems.
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state.Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach.The idea is tested by the two models, the transverse Ising model and the traveling salesman problem.Adding the transverse field to the Ising model is a simple way to introduce quantum fluctuations.The strength of the transverse field is controlled as a function of time similarly to the temperature in the conventional method.The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible.We also consider the traveling salesman problem.This model can be described by the Ising spin, so that we also apply the same technique to the transverse Ising model.We solve the time-dependent Schrödinger equation numerically for small size systems with various types of exchange interactions of the Ising model.Comparison with the results of the corresponding classical (thermal) method reveals that the quantum method leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule of the control parameters.We check the case of large-size systems by using the quantum Monte Carlo method.The simulation supports the results of the small-size systems, while the dynamics of the Schrödinger equation and the quantum Monte Carlo method are not the same.We find that the simulated annealing by quantum fluctuations has a better performance than the conventional method for the ground state search of the Ising-spin systems.The calculation of the traveling salesman problem is also performed as A.3 Case of Γ(t) = c/ √ t . . . . . . . . . . . . . . . . . . . . . . . .
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.