Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Induced representations of the two-parameter Jordanian quantum algebra

We construct induced infinite-dimensional representations of the two-parameter quantum algebraUg,h(gl(2)) which is in duality with the deformationGLg,h(2). The representations depend on two representation parameters, but split into one-parameter representations of a one-generator central subalgebra and the three-generator Jordanian quantum subalgebraU (sl(2)), =g + h. The representations of the latter can be mapped to representations in one complex variable, which give anew deformation of the standard one-parameter vector-field realization ofsl(2). These infinite-dimensional representations are reducible for some values of the representation parameters, and then we obtain canonically the finite-dimensional representations ofU (sl(2)). Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Permanent address of V.K.D.     

Image states on beryllium surfaces with low indices

Using the self-consistent pseudopotential method, we have calculated the binding energy of the image states for the (0001) , and surfaces of beryllium. It is shown for the (0001) face that there exists a pronounced resonance image state with n=1 and energy −0.95 eV at the point of the surface Brillouin zone. In the surface, which has a wide band gap in the vicinity of the vacuum level, the calculated image state with n=1 at the point has energy −1.2 eV and is a surface state of gap type. For the face in the vicinity of the point band gaps are absent. However, the symmetry of the bulk states near the vacuum level enables the existence of a resonance image state with n=1 and energy −0.6 eV. Fiz. Tverd. Tela (St. Petersburg) 41, 935–940 (June 1999)     

Tunneling Across an Inhomogeneous Delta-Barrier

The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy (where 0$$ " align="middle" border="0"> and 0$$ " align="middle" border="0"> are two constants). In particular, the perpendicular incidence of an electron with a given value of the wave vector is considered. The electron is forward-scattered into the region behind the barrier (region 2: 0$$ " align="middle" border="0"> ), i. e. the wave function is composed of plane waves with all wave vectors such that and \left. 0 \right)} $$ " align="middle" border="0"> ) (where ). Therefore, if 0$$ " align="middle" border="0"> , the wave function of the electron is represented as , where . An approximate formula is derived for the amplitude . The authors pay a special attention to the flow density and calculate this function in two cases: 1. for the plane and 2. for high values of is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier.     

Observation of a new surface state on4He crystal interfaces

The equilibrium shape ofhcp ⁴He crystals has been studied at temperatures 0.05≤T≤0.7 K by means of a high precision optical interferometer. We find that the profile of the interfacial boundary, close to an almost horizontal c-facet, has a well-defined slope discontinuity separating two angular regions with different behavior of the surface stiffness. For surfaces tilted by an angle ϕ≤100 μrad with respect to the c-facet, we obtain, contrary to the linear angular dependence predicted by current theories.     

Total Electron Emission from Metals Due to the Impact of Highly-Charged Xe Ions with Energies Up to MeV

Total electron emission from metals due to the impact of multiply charged ions, , may significantly influence quantitative measurements of ion current in corpuscular diagnostics. The value of (/q) was determined for Xe ions impacting clean polycrystalline copper as a function of ion charge state and of ion kinetic energy, keV/q, i.e. in the energy region up to keV/amu, where there is a lack of such data. For highly charged projectile ions, was found to have a clear minimum as a function of E _i. With decreasing charge state of the projectile ion this minimum shifts to a lower energy and becomes shallower. This observation is in agreement with compiled results of other authors. Limits for values of are estimated and discussed.     

Representations of \mathcal{U}_q (sl(3)) at roots of 1 (In the restricted specialisation)

Irreducible representations of at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra not to be completely diagonalised. Some irreducible representations of indeed contain indecomposable -modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation.     

Using the e ± μ? + E Tmiss signature in the search for supersymmetry and lepton-flavor violation in neutralino decays

The LHC (CMS) discovery potential in the search for supersymmetry and lepton-flavor violation in neutralino decays using the e ^± μ^∓ + E _T ^miss signature is studied. A detailed study is done for the CMS test points LM1-LM9. It is shown that, for the point LM1, it is possible to detect lepton-flavor violation in neutralino decays with lepton-flavor-violating branching Br( → μ^± e ^∓ ) ≥ 0.04 Br( → e ⁺ e ⁻ , μ⁺ μ⁻ ) for an integral luminosity of 10 fb⁻¹. The discovery potential in the mSUGRA-SUSY scenario with tan β = 10, sgn(μ) = + in the (m ₀, m _1/2) plane using the e ^± μ^∓ + E _T ^miss signature is determined. The text was submitted by the authors in English.     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).     

Double quantization on the coadjoint representation of sl(n)

For we construct a two parametric -invariant family of algebras, , that is a quantization of the function algebra on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric -invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on .     

Effect of a magnetic field on the yield point of NaCl crystals

A constant magnetic field is found to have a substantial effect on the macroplasticity of NaCl crystals when they are being actively strained at a constant rate during magnetic treatment. We have measured the dependence of the yield point σ _y on the magnetic induction B=0–0.48 T and the strain rate . It is shown that this magnetic effect has a threshold character and is observed only for B>B _c , where B _c grows with increasing as . The lower the strain rate , the larger the relative decrease in the yield point σ _y (B)/σ _y (0) at fixed field B>B _c . At small enough strain rates the threshold field B _c ceases to depend on and goes constant. A theoretical model is proposed which is in good agreement with the observed regularities. The model is based on the competition between thermally activated and magnetically stimulated depinning of dislocations from paramagnetic impurity centers. Zh. éksp. Teor. Fiz. 115, 951–958 (March 1999)     

Weakly non-Hermitian square well

Inside a box of size L we contemplate the simplest -symmetric piece-wise constant potential of size ℓ < L and purely imaginary strength ig and describe all its bound states in closed form. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Comparative analysis of real and \mathcal{P}\mathcal{T}-symmetric Scarf potentials

The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle the two potentials separately both in the conventional Hermitian and in the -symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy eigenvalues. Several main differences between the -symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number, the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of symmetry and the non- orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the corresponding Hermitian systems are also pointed out.     

Evidence for non-q \bar q mesons

The non-Abelian nature of QCD suggests that particles that have a gluon constituent, such as glueballs or hybrids, should exist. In addition,q q states are also predicted. This paper describes a search for these non-q q mesons performed by experiment WA 76 using the CERN Omega Spectrometer and discusses three candidates which have been observed.Invited talk at HEXAM 89, Bechyn Castle, Czechoslovakia, June 25–30, 1989.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.