Equivalence of the Sutherland Model to Free Particles on a Circle

A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the $N$-particle Sutherland model, with pair-wise inverse sine-square interactions among the particles, is shown to be equivalent to free particles on a circle. Applicability of our method to many other few and many-body problems is also illustrated.Comment: 12 pages, REVTeX, some typographical errors and few mistakes in the references are corrected. Few comments are adde

Induced magnetic moment in noncommutative Chern-Simons scalar QED

We compute the one loop, $O(\th)$ correction to the vertex in the noncommutative Chern-Simons theory with scalar fields in the fundamental representation. Emphasis is placed on the parity odd part of the vertex, since the same leads to the magnetic moment structure. We find that, apart from the commutative term, a $\th$-dependent magnetic moment type structure is induced. In addition to the usual commutative graph, cubic photon vertices also give a finite $\th$ dependent contribution. Furthermore, the two two-photon vertex diagrams, that give zero in the commutative case yield finite $\th$ dependent terms to the vertex function.Comment: 8 pages, 8 figures. Reference added. A remark about hep-th/0410257, in the original version, changed after clarification from the author

Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry

The one-loop contribution to vacuum polarization is calculated for the adjoint fermions in three dimensional noncommutative spaces, both at zero and finite temperature. At zero temperature, we confirm a previously found result for the parity odd part and subsequently analyze the even parity part, which exhibits UV/IR mixing. We discuss in detail, two regimes of the high temperature behavior of the parity odd part. When the thermal wavelength is much smaller, as compared to the noncommutativity scale, we find an interesting Fermi-Bose transmutation in the nonplanar part.Comment: 15 pages, minor corrections and references added (version to appear in JHEP

Comment on "Comment on 'Supersymmetry, PT-symmetry and spectral bifurcation'"

In "Comment on Supersymmetry, PT-symmetry and spectral bifurcation" \cite{BQ1}, Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in \cite{AP}. However, in the spontaneously broken PT-symmetry case, their argument is incorrect since it fails to implement the condition for the potential to be PT-symmetric: $C^{PT}[2(A-B)+\alpha]=0$. It needs to be emphasized that in the models considered in \cite{AP}, PT is spontaneously broken, implying that the potential is PT- symmetric, whereas the ground state is not. Furthermore, our supersymmetry (SUSY)-based 'spectral bifurcation' holds \textit{independent} of the $sl(2)$ symmetry consideration for a large class of PT-symmetric potentials.Comment: 2 page

Chirp Control of Sinusoidal Lattice Modes in Bose-Einstein Condensate

A parametrically forced Bose-Einstein condensate (BEC) is studied in the mean field approach for the case of a general moving optical lattice. The interaction between the atoms in the condensate and the time dependent lattice potential leads to a novel propagating superfluid matter wave, which can be controlled through chirp management. This system, when placed in a trap, accelerates and undergoes rapid nonlinear compression, controlled by the chirp. The density achieves its maximum, precisely when the matter wave changes direction. A dynamical phase transition is identified, which takes the superfluid phase to an insulating state. The exact expression for energy is obtained and analyzed in detail to gain physical understanding of the chirp management of the sinusoidal excitations and also the dynamical phase transition.Comment: This Paper has been withdrawn by the authors. An extensive modified version of this paper can be found at arXiv:1506.0079

Quantum information splitting using multi-partite cluster states

We provide various schemes for the splitting up of Quantum information into parts using the four and five partite cluster states. Explicit protocols for the Quantum information splitting (QIS) of single and two qubit states are illustrated. It is found that the four partite cluster state can be used for the QIS of an entangled state and the five partite cluster state can be used for QIS of an arbitrary two qubit state. The schemes considered here are also secure against certain eavesdropping attacks.Comment: 7 Page

N-qubit Quantum Teleportation, Information Splitting and Superdense Coding through the composite GHZ-Bell Channel

We introduce a general odd qubit entangled system composed of GHZ and Bell pairs and explicate its usefulness for quantum teleportation, information splitting and superdense coding. After demonstrating the superdense coding protocol on the five qubit system, we prove that '2N +1' classical bits can be sent by sending 'N+1' quantum bits using this channel. It is found that the five-qubit system is also ideal for arbitrary one qubit and two qubit teleportation and quantum information splitting (QIS). For the single qubit QIS, three different protocols are feasible, whereas for the two qubit QIS, only one protocol exists. Protocols for the arbitrary N-qubit state teleportation and quantum information splitting are then illustrated.Comment: 8 pages, 6 table

Controlled Spin Transport in Planar Systems Through Topological Exciton

It is shown that a charge-neutral spin-1 exciton, realizable only in planar systems like graphene, can effectively be used for controlled spin transport in such media. The excitonic bound state is destabilized by quantum fluctuations, characterized by a threshold for excitation and melts in a smooth manner under thermal fluctuations. This planar exciton differs from the conventional ones, as it owes its existence to the topological Chern-Simons (CS) term. The parity and time-reversal violating CS term can arise from quantum effects in systems with parity-breaking mass-gap. The spinning exciton naturally couples to magnetic field, leading to the possibility of controlled spin transport. Being neutral, it is immune to adverse effects, afflicting spin transport by charged fermions.Comment: 9 pages, 3 figures, References upgrade

Soliton Solutions of the σ\sigma Model and the Disoriented Chiral Condensates

We derive travelling soliton solutions of the $\sigma$ model, relevant for the description of dynamics of pions, in the high-energy, heavy-ion collisions. These extended objects are analogs of Ne$\grave{e}$l and Bloch type defects in ferromagnetic systems and could possibly describe the disoriented chiral condensates. It is shown that these solutions are metastable and can naturally produce an asymmetry between $\pi^0$ and $\pi^+$, $\pi^-$ mesons in the soft-pion emissions from heavy-ion collisons.Comment: 4 pages, LaTex, invited talk presented at workshop SOLITONS: properties, dynamics, interactions and applications, held at Kingston, Ontario, Canada, July 20 - Jul 26, 199

Quantum and Thermal Fluctuations and Pair-breaking in Planar QED

Planar quantum electrodynamics, in presence of tree-level Chern-Simons term, is shown to support bound state excitations, with a threshold, not present for the pure Chern-Simons theory. In the present case, the bound state gets destabilized by vacuum fluctuations. The bound state itself finds justification in the duality of the theory with massive topological vector field. Thermal fluctuations further destabilize this state, leading to smooth dissociation at high temperatures. Physical systems are suggested for observing such a bound state.Comment: 16 pages, 3 figures. Concepts are further elucidate