Quantum mechanics on topologically nontrivial spaces

The formulation of quantum mechanics on topologically nontrivial spaces is discussed. It is pointed out that the obstacles are represented by cohomology groups and not only by ₁(m) as usually stated. Some widespread errors and misunderstandings are cleared up.     

Kinematical properties of topologically nontrivial models of space-time

Using simple geometric models of wormholes as examples, we analyze the influence of the boundary conditions arising as a result of sewing the inner and outer spaces, on the casual structure of space-time and clock synchronization. It is shown that the relativity principle cannot be applied to the motion of the wormhole in the outer space. We demonstrate that it is impossible to dynamically transform a wormhole into a time machine. It is noted that the considered models are counterexamples to a number of statements concerning causality violation.VMTs Integral. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 83–88, December, 1992.     

Particle statistics in topologically nontrivial two-dimensional magnetic systems

It is demonstrated that charged particles may acquire unusual statistics in topologically nontrivial two-dimensional samples placed in strong magnetic fields. These novel statistics follow from an analysis of the self-adjoint extensions of the Landau hamiltonian which are partially classified by the UIR's of the fundamental group. Superselection rules corresponding to different quantum theories are found. Supersymmetry arguments are used to construct exact ground states.     

Effective construction of topologically nontrivial solutions in general relativity

In this study we propose a method for obtaining a closed solution of the Einstein-Maxwell equations in the case that arbitrary stationary solitons are generated on the arbitrary static background. In particular, we demonstrate that the already existing single-sheet solutions only form a subclass of the manifold of all the solutions, which in general are multisheet-like and have a nontrivial topology.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 75–81, September, 1986.The authors are grateful to M. Zarinov for discussions about some questions in this work.     

Spinor fields on 2 + 1 topologically nontrivial spacetime

Zeta-function regularization is used to evaluate the vacuum energy for a spinor field defined on a space-time of the formR ×H ²/,H ² being the Lobatchevsky plane and a strictly hyperbolic discrete subgroup ofPSL(2,R). The necessary analytic continuation is performed making use of the Selberg trace formula.     

Phase Dynamics at the SQUID and Macro-Realism

Taking into account some philosophical notionson realism a reformulation ofmacro-realism according to Leggett-Garg isput forward. A macroscopic phase dynamics based on amicroscopic SQUID-model is discussed in this context.     

Passage from spin-polarized surface states to unpolarized quantum well states in topologically nontrivial Sb films

Topological materials have unusual surface spin properties including a net surface spin current protected by the bulk symmetry properties. When such materials are reduced to thin films, their gapless spin-polarized surface states must connect, by analytic continuation, to bulk-derived quantum-well states, which are spin-unpolarized in centrosymmetric systems. The nature of this passage in a model system, Sb films, is investigated. Angle-resolved photoemission shows a smooth transition, while calculations elucidate the correlated evolution of the spin and charge distributions in real space.     

Stochastic Resonance for a SQUID with Dichotomous Resistance

We investigate the response to the ac current for a superconducting quantum interference device （SQUID） with a dichotomous resistance. It is shown that, for some suitably selected parameters＇ values, stochastic resonance appears for the amplitude of the stationary average voltage of the SQUID versus the correlation time of the dichotomous noise. Our result can provide some useful insights for the investigation of the response of the SQUID （especially for the ones with the nano junctions） to the temporal-periodic signal （including the input ac current, the irradiation microwave, the detected temporal-periodic signal, and the added ac voltage）.     

QCD as a topologically ordered system

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ$\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1)_A$U{\left(1\right)}_A$ problem where the would be η^′${\eta }^{\prime }$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1)_A$U{\left(1\right)}_A$ problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations.     

Three-qubit quantum-gate operation with an SQUID in a cavity

We propose a method of realizing a three-qubit quantum gate with a superconducting quantum interference device(SQUID) in a cavity.In this proposal,the gate operation involves the SQUID ground-states and the Fock states of cavity modes b and c.The two field-modes act as the controlling qubits,and the two SQUID states form the target qubit.Since only the metastable lower levels are involved in the gate operation,the gate is not affected by the SQUID decay rates.     

Subalgebras of the algebra of a conformal group with nontrivial center

A similarity relationship is set up in the set of subalgebras with a nontrivial center of a conformal group algebra that separates it into classes of mutually similar subalgebras. In all 24 different classes of similar subalgebras are obtained and one representative is described in each class. All the nonequivalent two-dimensional commutative subalgebras of a conformal group algebra are obtained as an illustration of applying such a subalgebra system. The results of the research can be used to obtain the solutions of conformally invariant equations in the separated variables.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 45–48, May, 1990.     

Dipole clusters with nontrivial scale-invariant properties

In this paper the scale-invariant properties of the plane (2D) with the growth centre located on the charged particle have been considered. The dependence “number of particles with respect to radius of cluster” is presented by two power-law exponents that differs them from one power-law dependence characterizing the DLA (diffusion limited aggregation) clusters. In our case the interpretation the power-law exponents found in terms of the fractal dimension becomes unacceptable. The model considered it is supposed to be applied for consideration of similar clusters in polar liquids.     

Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a singlequbit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-l/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.     

Collective properties of superconductors with nontrivial pairing

Three-and two-dimensional models of p-and d-pairing are constructed for superconductors and superfluid quantum liquids using the functional integration formalism. In these models, the collective excitation spectra are calculated for superconductors with nontrivial pairing (such as high-temperature superconductors (HTSC) and heavy-fermion superconductors (HFSC)) for p-and d-pairing. Both three-and two-dimensional systems are considered. Some of recent ideas concerning the realization of the mixture of different states in HTSC are considered. In particular, the mixture of states $d_{x^2 - y^2 } + id_{xy} $ is analyzed. The obtained results of calculations of collective excitation spectra in superconductors with nontrivial pairing may be used for determining the type of pairing and the order parameter in HTSC and HFSC and also for interpreting the experimental results on ultrasound and microwave absorption in these system.