Related papers: Theta Correspondence and Quantum Induction
We show that under suitable assumptions, we have a one-to-one correspondence between classical groups and free quantum groups, in the compact orthogonal case. We classify the groups under correspondence, with the result that there are…
Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution…
Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations $\sigma$ of unitary groups and investigate their relation with the occurrence of a simple global…
We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite $\hbar_{\rm eff}$ values in…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
Let $\Pi_0$ be a representation of a group $H$. We say that a representation $\tau$ is $(H,\Pi_0)$-distinguished, if it is a quotient of $\Pi_0$. It is natural to ask whether this notion "inflates" to larger groups, in the sense that a…
Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used but the validity of reduction of a quantum problem to a classical problem…
We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
We propose an approach to the quantum-classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and…
There is a huge amount of work on different kinds of theta functions, the theta correspondence, cohomology classes coming from special Schwartz classes via theta distribution, and much more. The aim of this text is to try to find joint…
Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is…
A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and…
Based on previous studies in a single particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys.~Rev.~X {\bf 5}, 031038 (2015)] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys.~Rev.~E {\bf 93}, 062108 (2016)], we study…
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
Induction is typically formalized as a rule or axiom extension of the LK-calculus. While this extension of the sequent calculus is simple and elegant, proof transformation and analysis can be quite difficult. Theories with an induction…