Performance comparison between classical and quantum control for a simple quantum system

Brańczyk et al. pointed out that the quantum control scheme is superior to the classical control scheme for a simple quantum system using simulation [A.M. Brańczyk, P.E.M.F. Mendonca, A. Gilchrist, A.C. Doherty, S.D. Barlett, Quantum control theory of a single qubit, Physical Review A 75 (2007) 012329 or arXiv e-print quant-ph/0608037]. Here we rigorously prove the result. Furthermore we will show that any quantum operation does not universally “correct” the dephasing noise.     

Delay-time statistics for diffuse waves

We formulate a theory for the statistics of the dynamics of a classical wave propagating in random media by analyzing the frequency derivative of the phase under the assumption of a Gaussian process. We calculate frequency correlations and probability distribution functions of dynamical quantities, as well the first non-Gaussian C2 correction. In A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, Phys. Rev. Lett. 82, 715 (1999), microwave measurements have been performed to which this theory applies.     

Dirac Operator on the Podleś Sphere

The spectral problem for the Dirac operator on the Podle sphere is discussed and solved in one of its possible formulations. The standard constructions for the Dirac operator on classical symmetric spaces and the spectrum of the Dirac operator on the classical two-dimensional sphere are recalled. The problem of defining a spinor structure on a quantum space is discussed and the definitions of a classical spinor structure and Dirac operator according to Ðurdevich are sketched. The Dirac operator for the Podles´ quantum sphere treated as a quotient space of SU(2) is constructed using the Woronowicz left-covariant calculus over this quantum group. The spectrum of the operator is obtained. Disagreement of its asymptotic behavior with Connes' axiom of noncommutative spectral geometry is stressed.     

Quantum projection. Integration of the open Tod quantum chain

A quantum projection method is developed on the basis of noncommutative integration of linear differential equations and the results of M. A. Ol’shanetskii and A. M. Perelomov on the integration of classical Hamiltonian systems (projection method). The method proposed makes it possible to obtain in explicit form solutions of the quantum equations whose classical analogs can be integrated by projection. Then the semisimplicity property of the symmetry algebra of the original equation is no longer a factor. The solution basis of a Schrödinger equation with the potential of an open three-particle Tod chain is constructed as a nontrivial example.     

Non-Grassmannian approach to spinning particles II

A classical model of spinning particles, elaborated in a previous paper, is shown to be comparable with the conventional Grassmannian approach in two key respects: it leads to a unique value of spin 1/2 and the corresponding path integral is relatively simple, since it involves Dirac-functions.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank V. Balek, M. Fecko, P. Prenajder and M. Melek for useful discussions and J. Weiss for his constant encouragement.     

A theorem allowing to derive deterministic evolution equations from stochastic evolution equations

The deterministic evolution equations of classical as well as quantum mechanical models are derived from a set of stochastic evolution equations after taking an average over realizations using a theorem. Examples are given that show that deterministic quantum mechanical evolution equations, obtained initially by R.P. Feynman and subsequently studied by Boghosian and Taylor IV [B.M. Boghosian, W. Taylor IV, Phys. Rev. E 57 (1998) 54. See also arXiv:quant-ph/9904035] and Meyer [D.A. Meyer, Phys. Rev. E 55 (1997) 5261], among others, are derived from a set of stochastic evolution equations. In addition, a deterministic classical evolution equation for the diffusion of monomers, similar to the second Fick law, is also obtained.     

Classical oscillator with position-dependent mass in a complex domain

We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [A.V. Smilga, J. Phys. A 41 (2008) 244026, arXiv:0706.4064; A. Mostafazadeh, J. Math. Phys. 43 (2002) 205; A. Mostafazadeh, J. Math. Phys. 43 (2002) 2814; A. Mostafazadeh, J. Math. Phys. 43 (2002) 3944]. The role of PT-symmetry is discussed from the perspective of classical trajectories of CEO for real energy. Some trajectories of CEO are similar to those for the particle in a quartic potential in the complex domain [C.M. Bender, S. Boettcher, P.N. Meisinger, J. Math. Phys. 40 (1999) 2201; C.M. Bender, D.D. Holm, D. Hook, J. Phys. A 40 (2007) F793, arXiv:0705.3893].     

Classical stark mixing at ultralow collision energies

Exact solutions of the time-dependent classical equations are obtained for the full array of angular momentum mixing transitions nl-->nl(') in atomic hydrogen induced by collisions with charged particles at ultralow energies. A novel classical expression for the transition probability P(l(')l) is presented. The exact classical results for P(l(')l)(alpha) as a function of l,l(') and the Stark parameter alpha agree exceptionally well with (exact) quantal results. They complement the quantal results by revealing essential characteristics which remain obscured in the quantal treatment.     

Classical and quantum localization and delocalization in the Fermi accelerator,kicked rotor and two-sided kicked rotor models

The phenomena of dynamical localization, both classical and quantum, are studied in the Fermi accelerator model. The model consists of two vertical oscillating walls and a ball bouncing between them. The classical localization boundary is calculated in the case of "sinusoidal velocity transfer" [A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, Berlin, 1983)] on the basis of the analysis of resonances. In the case of the "sawtooth" wall velocity we show that the quantum localization is determined by the analytical properties of the canonical transformations to the action and angle coordinates of the unperturbed Hamiltonian, while the existence of the classical localization is determined by the number of continuous derivatives of the distance between the walls with respect to time. (c) 1996 American Institute of Physics.     

Force chain splitting in granular materials: A mechanism for large-scale pseudo-elastic behaviour

We investigate both numerically and analytically the effect of strong disorder on the large-scale properties of the hyperbolic equations for stresses proposed in J.-P. Bouchaud, M.E. Cates, P. Claudin, J. Phys. I 5, 639 (1995), and J.P. Wittmer, P. Claudin, M.E. Cates, J.-P. Bouchaud, Nature 382, 336 (1996); J.P. Wittmer, P. Claudin, M.E. Cates, J. Phys. I 7, 39 (1997). The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large-scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two-peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable. Received 13 November 2000 and Received in final form 3 January 2001     

周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.     

On the spin of Solitons in 2+1 dimensional models

It is believed that the charged vortex in the Chern-Simons-Higgs model can have fractional spin, since the extra angular momentum of the static vortex calculated from the classical energy-momentum tensor is nonzero. We re-examine the spin of the charged vortex by use of quantum mechanical method, by which the baby skyrmion in theO(3) nonlinear -model with the Hopf term is pointed out to have fractional spin. It is shown that the spin of the charged vortex obtained from the quantum mechanical argument does not necessarily coincide with the value of classical extra angular momentum. Moreover, it is found that its value is not unique, since it is one of quantities which depend on the gauge condition of the Chern-Simons gauge field.     

Conditional expectations,conditional distributions,anda posteriori ensembles in generalized probability theory

A general probabilistic framework containing the essential mathematical structure of any statistical physical theory is reviewed and enlarged to enable the generalization of some concepts of classical probability theory. In particular, generalized conditional probabilities of effects and conditional distributions of observables are introduced and their interpretation is discussed in terms of successive measurements. The existence of generalized conditional distributions is proved, and the relation to M. Ozawa'sa posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.     

Statistics of branched flow in a weak correlated random potential

Recent images of electron flow through a two-dimensional electron gas device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [M. A. Topinka, Nature 410, 183 (2001)]]. We show how such branching arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing statistical properties of the branching are confirmed by classical and quantum numerical tests.     

Comment on: “From classical to modern ether-drift experiments: the narrow window for a preferred frame” [Phys. Lett. A 333 (2004) 355]

In a recent article [M. Consoli, E. Costanzo, Phys. Lett. A 333 (2004) 355], M. Consoli and E. Costanzo have investigated classical and modern aether drift experiments and explored the narrow window for detection of a preferred reference frame. This Letter proposes an easy to perform variant of Fizeau's experiment, which may confirm or deny Consoli–Costanzo's claims.     

Noether symmetries and the quantization of a Liénard-type nonlinear oscillator

The classical quantization of a Liénard-type nonlinear oscillator is achieved by a quantization scheme (M. C. Nucci. Theor. Math. Phys., 168:994–1001, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation in the momentum space as given in (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light on the apparently remarkable connection with the linear harmonic oscillator.     

SINGAO: a very large telescope for neutrino gamma astronomy and cosmic-ray studies

Summary We discuss the feasibility of a telescope consisting in a sampling array for extensive air showers measure combined with a muon tracking device. The sampling array will extend over a surface of ≥10⁷ m² while the muon tracking device will cover ≥10⁴ m². The telescope should be done with resistive plates counters and would become a very powerful device to study high-energy neutrinos and gamma-ray astronomy as well as cosmicray physics up to the highest energy (≥10¹⁹ eV) region. The content of this paper has been elaborated with the following people interested in performing the experiment: M. De Palma, G. Iaselli, C. Maggi, S. Natali, S. Nuzzo, A. Ranieri, C. Raso, F. Romano, F. Ruggeri, G. Selvaggi, P. Tempesta, G. Zito; A. Rossi, G. Susinno; A. Grillo, F. Ronga, V. Valente; P. Bernardini, P. Pistilli; A. Watson, R. Reid, M. Lawrence; M. Ambrosio, G. Barbarino, B. Bartoli, V. Silvestrini; R. Buccheri, M. Carollo, O. Catalano, J. Linsley, L. Scarsi; G. Bressi, A. Lanza, M. Cambiaghi, S. Ratti; M. Bonori, G. D'Agostini; M. De Vincenzi, E. Lamanna, P. Lipari, G. Martellotti, F. Massa, M. Mattioli, A. Nigro, S. Petrera; R. Cardarelli, F. Rossi, R. Santonico; L. De Cesare, G. Grella, M. Guida, F. Mancini, G. Marini, G. Romano, G. Vitiello; C. Cappa, B. D'Ettore Piazzoli, P. Ghia, G. Gomez, P. Trivero. [Bari, Cosenza, Laboratori Nazionali di Frascati Lecce, Leeds, Napoli, Palermo, Pavia, Roma I, Roma II, Salerno, Torino, Istituto di Cosmogeofisica del CNR].     

Scattering in Supersymmetric M(atrix) Models

We review several tests of the M(atrix)‐Model conjecture that asserts that the dynamics of M‐Theory, the eleven‐dimensional Ur‐theory containing all known string theories and also eleven‐dimensional supergravity in specific limits, is given by a quantum mechanical matrix model. In particular, scattering processes are analyzed both from the M(atrix)‐Model and from the supergravity perspective and the corresponding S‐matrix elements are compared. We find impressive agreement between these two theories as long as only classical supergravity is considered. If one includes also quantum effects on the supergravity side, the agreement does not persist. In addition to these calculations, the question of the existence of classical solutions to the M(atrix)‐Model equations of motion with momentum transfer is addressed and answered negatively.