Quantum integrability of the deformed elliptic Calogero-Moser problem

The integrability of the deformed quantum elliptic Calogero-Moser problem introduced by Chalykh, Feigin and Veselov is proven. Explicit recursive formulae for the integrals are found. For integer values of the parameter this implies the algebraic integrability of the systems.Comment: 23 page

The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry

An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS_5xS^5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else unchange

Vacuum polarization induced by a uniformly accelerated charge

We consider a point charge fixed in the Rindler coordinates which describe a uniformly accelerated frame. We determine an integral expression of the induced charge density due to the vacuum polarization at the first order in the fine structure constant. In the case where the acceleration is weak, we give explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys

Street Gangs and Coercive Control: The Gendered Exploitation of Young Women and Girls in County Lines

This paper explores young women and girls’ participation in gangs and ‘county lines’ drug sales. Qualitative interviews and focus groups with criminal justice and social service professionals found that women and girls in gangs often are judged according to androcentric, stereotypical norms that deny gender-specific risks of exploitation. Gangs capitalise on the relative ‘invisibility’ of young women to advance their economic interests in county lines and stay below police radar. The research shows gangs maintain control over women and girls in both physical and digital spaces via a combination of threatened and actual (sexual) violence and a form of economic abuse known as debt bondage; tactics readily documented in the field of domestic abuse. This paper argues that coercive control offers a new way of understanding and responding to these gendered experiences of gang life, with important implications for policy and practic

Partition function of the eight-vertex model with domain wall boundary condition

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.Comment: Latex file, 20 pages; V2, references adde

Orienting coupled quantum rotors by ultrashort laser pulses

We point out that the non-adiabatic orientation of quantum rotors, produced by ultrashort laser pulses, is remarkably enhanced by introducing dipolar interaction between the rotors. This enhanced orientation of quantum rotors is in contrast with the behavior of classical paired rotors, in which dipolar interactions prevent the orientation of the rotors. We demonstrate also that a specially designed sequence of pulses can most efficiently enhances the orientation of quantum paired rotors.Comment: 7 pages, 5 figures, to appear in Phys. Rev.

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

Zero modes on cosmic strings in an external magnetic field

A classical analysis suggests that an external magnetic field can cause trajectories of charge carriers on a superconducting domain wall or cosmic string to bend, thus expelling charge carriers with energy above the mass threshold into the bulk. We study this process by solving the Dirac equation for a fermion of mass $m_f$ and charge $e$, in the background of a domain wall and a magnetic field of strength $B$. We find that the modes of the charge carriers get shifted into the bulk, in agreement with classical expectations. However the dispersion relation for the zero modes changes dramatically -- instead of the usual linear dispersion relation, $\omega_k =k$, the new dispersion relation is well fit by $\omega \approx m_f tanh(k/k_*)$ where $k_*=m_f$ for a thin wall in the weak field limit, and $k_*=eBw$ for a thick wall of width $w$. This result shows that the energy of the charge carriers on the domain wall remains below the threshold for expulsion even in the presence of an external magnetic field. If charge carriers are expelled due to an additional perturbation, they are most likely to be ejected at the threshold energy $\sim m_f$.Comment: 9 pages, 4 figure

Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again

We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys. Rev.