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We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…
This review covers the study of some basic properties of the phase diagram of quasi-one-dimensional organic superconductors from both experimental and theoretical viewpoints.
We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Links between supersymmetric classical and quantum mechanics are explored. Diagrammatic representations for \hbar-expansions of norms of ground states are provided. The WKB spectra of supersymmetric non harmonic oscillators are found.
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
A systematic method for calculating higher-order corrections of the relativistic semiclassical fixed-energy amplitude is given. The central scheme in computing corrections of all orders is related to a time ordering operation of an operator…
We show that the approximate quasiorthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum channels. Our analysis is based on a characterization of…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…
A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ for any given level $k$ is constructed in terms of three free boson fields and their accompanying twisted partners. It can be viewed as the elliptic deformation of…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in…
It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators one can take…
It has long been thought that strongly correlated systems are adiabatically connected to their noninteracting counterpart. Recent developments have highlighted the fallacy of this traditional notion in a variety of settings. Here we use a…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
We show that, for $N$ parallel input states, an anti-linear map with respect to a specific basis is essentially a classical operator. We also consider the information contained in phase-conjugate pairs $|\phi > |\phi^*>$, and prove that…