Related papers: New anatomy of quantum holonomy

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…

We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…

We introduce a fermionic formula associated with any quantum affine algebra U_q(X^{(r)}_N). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to…

We consider two-dimensional quantum gravity endowed with a positive cosmological constant and coupled to a conformal field theory of large and positive central charge. We study cosmological properties at the classical and quantum level. We…

We show that a recently introduced generalized scheme of quantum mechanics has connections to Li\'{e}nard and Levinson-Smith classes of nonlinear systems. For the Li\'{e}nard type, which has coefficients of odd and odd symmetry, we…

A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered…

A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…

We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…

Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…

Non-topological gauged soliton solutions called Q-balls arise in many scalar field theories that are invariant under a U(1) gauge symmetry. The related, but qualitatively distinct, Q-shell solitons have only been shown to exist for special…

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…

We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum…

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers…

We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant-ph/9904011), and reinforced by Fujii (quant-ph/9910069) and Pachos and Chountasis (quant-ph/9912093).…

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,…

We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the…