相关论文: Subsystem of neutral mesons beyond the Lee-Oehme-Y…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
We investigate the transition probabilities for the "flavor" eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the…
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded…
Let M be a Hamiltonian T space with a proper moment map, bounded below in some component. In this setting, we give a combinatorial description of the T-equivariant cohomology of M, extending results of Goresky, Kottwitz and MacPherson and…
A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator…
We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $\mathcal{N}$ with finite spectrum is analysed in detail. The…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
The weak-coupled two-level open quantum system described by non-Markovian Time-convolution-less master equation is investigated in this paper. The cut-off frequency, coupling constant and transition frequency, which impact on the system's…
This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of…
For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum…
If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly…
We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial…
We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger…
We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic…
We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on…
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…