Related papers: Geometric Phases and Mielnik's Evolution Loops
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
We perform a microcanonical study of classical lattice phi^4 field models in 3 dimensions with O(n) symmetries. The Hamiltonian flows associated to these systems that undergo a second order phase transition in the thermodynamic limit are…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
It is argued that renormalisation group flow can be interpreted as being a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate \lq\lq momenta", which are the vacuum expectation values…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
The wave description of geometric phase uses the superposition of light waves to explain the geometric phase's origin. While our previous work focused on a basis of linearly polarized waves, here we show that the same concepts can be…
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in…
The quantum dynamics generated by time-dependent variational calculations is discussed from the perspective of geometric quantization. On examples, it is shown that approximate energy eigenstates can be associated to the quantized periodic…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and non-cyclic (Mukunda-Simon)…