Spontaneous breakdown of $$ \mathcal{P}\mathcal{T} $$ symmetry in the complex Coulomb potential

The $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric, while the two independent solutions are transformed to each other by the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.     

Level crossings in complex two-dimensional potentials

Two-dimensional $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric quantum-mechanical systems with the complex cubic potential V ₁₂ = x ² + y ² + igxy ² and the complex Hénon-Heiles potential V _HH = x ² +y ² +ig(xy ² −x ³/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.     

Supersymmetric quantum mechanics living on topologically non-trivial Riemann surfaces

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H ^(±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian $ \mathcal{H} $ \mathcal{H} are defined along certain topologically non-trivial complex curves r ^(±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map $ \mathcal{T} $ \mathcal{T} between ‘tobogganic’ partner curves r ⁽⁺⁾(x) and r ⁽⁻⁾(x) is emphasized.     

Scarcity of real discrete eigenvalues in non-analytic complex $$ \mathcal{P}\mathcal{T} $$-symmetric potentials

We find that a non-differentiability occurring whether in real or imaginary part of a complex $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials x ² and |x| by imaginary $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric potentials ix/it|x| and ix, respectively.     

Production of strange secondaries in high-energy Σ<Superscript>−</Superscript><Emphasis Type="Italic">A</Emphasis> collisions

The WA89 Collaboration experimental data on production of Λ, Σ⁻, Σ⁺, Ξ⁻, Ω⁻ baryons, $ \bar \Lambda $ \bar \Lambda and $ \bar \Xi ^ + $ \bar \Xi ^ + antibaryons in Σ⁻ collisions with C and Cu targets at 345 GeV/c ($ \sqrt {s_{\Sigma N} } $ \sqrt {s_{\Sigma N} } ≈ 25.5 GeV) in the frame of the Quark-Gluon String Model is described. The comparison of the theoretical results with the experimental data is discussed. Finally, some relations among the values of the model parameters obtained with the help of quark combinatorics are presented.     

The property of maximal transcendentality in the N \mathcal{N} = 4 SYM

We show results for the universal anomalous dimension γ_uni(j) of Wilson twist-2 operators in the $ \mathcal{N} $ \mathcal{N} = 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

Complexification of three potential models — II

A new kind of $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} and non-$ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric complex potentials are constructed from a group theoretical viewpoint of the sl(2,C) potential algebras. The real eigenvalues and the corresponding regular eigenfunctions are also obtained. The results are compared with the ones obtained before.     

On the two-loop $$ \ma thcal{O} $$( αs2) correc tions to the pole mass of the t quark in the MSSM

The paper is devoted to the calculation of two-loop (α _s ²) MSSM corrections to the relation between the pole mass of the t quark and its running mass in the scheme. Firstly, the value of the second-order contribution from large-mass expansion in mt/M _SUSY is studied. Contrary to our expectations, this contribution turned out to be negligible. As a by-product of this calculation, the two-loop anomalous dimension of the running quark mass is obtained in the supersymmetric QCD. Secondly, the influence of the two-loop corrections to the t-quark mass on the predicted superpartner masses is investigated. The text was submitted by the authors in English.     

The p/π ratio pT dependence in the RHIC range of baryo-chemical potential

The BRAHMS measurement of proton-to-pion ratios in Au+Au and p+p collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV and $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV is presented as a function of transverse momentum and collision centrality within the pseudorapidity range 0 ≤ η ≤ 3. The baryo-chemical potential, μ _B , for the indicated data spans from μ _B ≈ 26 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 200 GeV, η ≈ 0) to μ _B ∼ 260 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV, η ≈ 3) [1]. The p/πratio measured for Au+Au system at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 62.4 GeV, η ≈ 3 reaches astounding value of 8–10 at p _T > 1.5 GeV/c. For these energy and pseudorapidity interval no centrality dependency of p/π ratio is observed. Moreover, the baryon-to-meson ratio of nucleus-nucleus data are consistent with results obtained for p+p interactions.     

Twist deformations of the supersymmetric quantum mechanics

The $ \mathcal{N} $ \mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even $ \mathcal{N} $ \mathcal{N} one can identify the 1D $ \mathcal{N} $ \mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.     

Laser-induced optical activity in range of Rydberg autoionizing states of xenon

Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically. The optical activity arises in the vicinity of the autoionizing state 5p ⁵(² P _1/2)8s′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 as a result of its coupling via the laser field with the discrete state 5p ⁵(² P _3/2)7p $ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 . Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with the broad autoionizing state 5p ⁵(² P _1/2)6d′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 induced by the overlap of the Rydberg autoionizing series in xenon are studied.     

Wakimoto realization of drinfeld current for the elliptic quantum algebra Uq,p( $$ \widehat{sl_3 } $$ )

We study a free field realization of the elliptic quantum algebra U_q,p($ \widehat{sl_3 } $ \widehat{sl_3 } ) for arbitrary level k. We give the free field realization of elliptic analog of Drinfeld current associated with U_q,p($ \widehat{sl_3 } $ \widehat{sl_3 } ) for arbitrary level k. In the limit p → 0, q → 1 our realization reproduces Wakimoto realization for the affine Lie algebra $ \widehat{sl_3 } $ \widehat{sl_3 } .     

Parton transverse momentum distribution at the moment of hadronization at RHIC

We extract the transverse momentum distribution of effective partons using the spectra of Ω, Ξ, Λ and ϕ hadrons measured by the STAR Collaboration from Au + Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV at RHIC. The extracted momentum distribution of strange quarks is flatter than that of up/down quarks consistent with hydrodynamics expansion in partonic phase prior to hadronization. Consistency in quark ratios derived from various hadron spectra gives clear evidence for hadron production as suggested by quark coalescence or recombination model.     

Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

New quasi-exactly solvable Hermitian as well as non-Hermitian $$ \mathcal{P}\mathcal{T} $$-invariant potentials

We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as well as $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender-Dunne polynomials.     

Compactons in PT \mathcal{P}\mathcal{T} -symmetric generalized Korteweg-de Vries equations

This paper considers the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric equations a general theorem relating the energy, momentum and velocity of any solitarywave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting the nonlinearities.     

Directed flow of identified particles from Au+Au collisions at RHIC

We present the measurement of directed flow (v ₁) for the identified particles, namely, Λ, $ \bar \Lambda $ \bar \Lambda and K _s ⁰, as a function of rapidity and centrality in Au+Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV and 62.4 GeV. The measurement is based on the run IV data obtained by the STAR experiment at RHIC. In order to enhance event plane resolution, we use tracks reconstructed from the Forward Time Projection Chambers (FTPCs), together with the sideward deflection of spectator neutrons measured by the STAR’s Shower Maximum Detector at Zero Degree Calorimeters (ZDC-SMDs). We find that for 200 GeV, proton and antiproton v ₁ is less than 1%, the K _s ⁰ Λ, $ \bar \Lambda $ \bar \Lambda v ₁ is less than 2%; for 62 GeV, proton v ₁ is less than 1% and antiproton is less than 2%, v ₁ for K _s ⁰, Λ, $ \bar \Lambda $ \bar \Lambda is less than 2% in Au+Au collisions at 200 GeV.     

Classical and quantum mechanics of complex hamiltonian systems: An extended complex phase space approach

Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation x = x ₁ + ip ₂, p = p ₁ + ix ₂, are revisited. It is argued that Carl Bender inducted $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry in the studies of complex power potentials as a particular case of the present general framework in which two additional degrees of freedom are produced by extending each coordinate and momentum into complex planes. With a view to account for the subjective component of physical reality inherent in the collected data, e.g., using a Chevreul (hand-held) pendulum, a generalization of the Hamilton’s principle of least action is suggested.     

Maximal possible accretion rates for slim disks

It was proved in the previous work that there must be a maximal possible accretion rate $ \dot M_{max} $ \dot M_{max} for a slim disk. Here we discuss how the value of $ \dot M_{max} $ \dot M_{max} depends on the two fundamental parameters of the disk, namely the mass of the central black hole M and the viscosity parameter α. It is shown that $ \dot M_{max} $ \dot M_{max} increases with decreasing α, but is almost independent of M if $ \dot M_{max} $ \dot M_{max} is measured by the Eddington accretion rate $ \dot M_{Edd} $ \dot M_{Edd} , which is in turn proportional to M.