Related papers: Non-adiabatic holonomy operators in classical and …
We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type, where the time 't' is also an operator. An effective commutative description of the system gives a time dependent…
The theory of adiabatic invariants has a long history and important applications in physics but is rarely rigorous. Here we treat exactly the general time-dependent 1-D harmonic oscillator, $\ddot{q} + \omega^2(t) q=0$ which cannot be…
Recently developed parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetric non-Hermitian quantum theory is envisioned to have far-reaching implications in basic science and applications. It is known that the $PT$-inner product is…
In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system…
Adiabatic evolution is an emergent design principle for time modulated metamaterials, often inspired by insights from topological quantum computing such as braiding operations. However, the pursuit of classical adiabatic metamaterials is…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse…
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By…
A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra…
The line bundles which arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel-Weil-Bott theorem of the representation theory. The remarkable relation of…
Non-perturbative partition functions of quantum theories constitute a class of $\tau-$functions, which are distinguished satisfying Hirota's bilinear identities(BI). To make this statement general, there must be a proper definition of…
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various…
The proposal of the optical scheme for holonomic quantum computation is evaluated based on dynamical resolution to the system beyond adiabatic limitation. The time-dependent Schr\"{o}dinger equation is exactly solved by virtue of the…
Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies, alike. Intriguingly, the exotic statistics of anyons realised in physical systems can be…
We proved a KAM theorem on existence of invariant tori in generalized Hamiltonian systems without action-angle variables. It is a generalization of the result of de la Llave et al. [Llave, 2005] that deals with canonical Hamiltonian system.
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
Complex quantum systems are often multiscale in nature with strong interactions between different scales. We present a novel idea: iteratively suppressing, rather than tracing out, the fast, high-energy degrees of freedom in strongly…
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems,…