Related papers: Adiabatic driving and geometric phases in classica…
The path dependence of adiabatic evolution in classical harmonic chains with clamps is examined. It is shown that cutting and joining a chain may braid adiabatic normal mode frequencies. Accordingly, different adiabatic paths with the same…
The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases…
This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
The force exerted by the electrons on the nuclei of a current-carrying molecular junction can be manipulated to engineer nanoscale mechanical systems. In the adiabatic regime a peculiarity of these forces is negative friction, responsible…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
We introduce a new way of generating the quantum geometric phase by making the initial base state index dependent on space-time curvature. We prove that the resulting Schr\"odinger equation is identical to the trace form of the Einstein…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
Motivated by the $\Omega$-spectrum proposal of unique gapped ground states by Kitaev, we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by…
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to…
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. Here, we show that for nonadiabatic dynamics with two…
We study quantum dynamics of Grover's adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolutions are visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the…
The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or…
A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path…