Related papers: Eigenvalue and eigenspace anholonomies in hierarch…
A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.
Holonomic quantum computation uses non-Abelian geometric phases to realize error resilient quantum gates. Nonadiabatic holonomic gates are particularly suitable to avoid unwanted decoherence effects, as they can be performed at high speed.…
Motivated by some recent results, we consider the notion of eigenstate (and eigenvalue) for an element $X$ of a CQ*-algebras and the consequences on algebraic quantum dynamics and on its related derivations are investigated.
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…
The article reviews the theory of open quantum system from a perspective of the non-Hermiticity that emerges from the environment with an infinite number of degrees of freedom. The non-Hermiticity produces resonant states with complex…
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling.…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
A class of time independent and physically meaningful Hamiltonians leads to evolution of observable quantities whose Ehrenfest times are arbitrarily large. This fact contradicts the popular claim that the true chaos is in quantum mechanics…
Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when…
The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time…
We show that a composite quantum system described by the tensor product of multiple systems each with a leading-order exceptional point (a non-Hermitian degeneracy at which not only eigenvalues but also eigenstates coalesce) exhibits a…
Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in presence of a free scalar field with, in turn, a negative cosmological…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with…