Supersymmetry and PT-Symmetric Spectral Bifurcation

Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a general scenario. It is found that, in an appropriate parameter domain, the ground state may or may not respect PT-symmetry. Interestingly, in the domain where PT-symmetry is not respected, two superpotentials give rise to one potential; whereas when the ground state respects PT, this correspondence is unique. In both scenarios, supersymmetry and shape-invariance are intact, through which one can obtain eigenfunctions and eigenstates exactly. Our procedure enables one to generate a host of complex potentials which are not PT-symmetric, and can be exactly solved.Comment: 9 page

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

Interference Aligned Space-Time Transmission with Diversity for the 2×22 \times 2 X-Network

The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multiple-output (MIMO) X-Network ($2 \times 2$ MIMO X-Network) with $M$ antennas at each node is known to be $\frac{4M}{3}$. Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for $M=2,4$. These schemes have been proven to guarantee a diversity gain of $M$ when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achieves the $\frac{4M}{3}$ sum-DoF of the $2 \times 2$ X-Network for arbitrary $M$ is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme which requires the availability of global CSIT in order to achieve the $\frac{4M}{3}$ sum-DoF. Further, it is shown analytically that the proposed scheme guarantees a diversity gain of $M+1$ when finite-sized input constellations are employed.Comment: Single Column, 32 pages, 4 figures; typos in the previous version fixe

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

Origin of Lattice Spin in Graphitic Systems

Lattice spin, in planar condensed matter system with emergent Dirac dispersion, is shown to emerge from the inherent SU(2) symmetry, arising through Schwingers angular momentum construction from anti-commuting Heisenberg operators of the sub-lattices. The presence of a mass term in the emergent Dirac dispersion is essential for the existence of this spin. The usual hopping term, that entangles the two sub-lattices, leads to the orbital counterpart. Relative sub-lattice displacements, that couple to the effective Dirac fermions like U(1) gauge fields, do not effect the lattice spin.Comment: 4 page

Suppressing phonon transport in nanowires: a simple model for phonon-surface roughness interaction

Suppressing phonon propagation in nanowires is an essential goal towards achieving efficient thermoelectric devices. Recent experiments have shown unambiguously that surface roughness is a key factor that can reduce the thermal conductivity well below the Casimir limit in thin crystalline silicon nanowires. We use insights gained from the experimental studies to construct a simple analytically tractable model of the phonon-surface roughness interaction that provides a better theoretical understanding of the effects of surface roughness on the thermal conductivity, which could potentially help in designing better thermoelectric devices.Comment: 7 pages, 3 figures; accepted for publication in Phys. Rev.

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

From particle in a box to PT -symmetric systems via isospectral deformation

A family of PT -symmetric complex potentials is obtained, which is isospectral to free particle in an infinite complex box in one dimension (1-D). These are generalizations to the cosec2 (x) potential, isospectral to particle in a real infinite box. In the complex plane, the infinite box is extended parallel to the real axis having a real width, which is found to be an integral multiple of a constant quantum factor, arising due to boundary conditions necessary for maintaining the PT -symmetry of the superpartner. As the spectra of the particle in a box is still real, it necessarily picks out the unbroken PT -sector of its superpartner, thereby invoking a close relation between PT -symmetry and SUSY for this case. As expected, the broken PT -sector has no isospectrality with any real system.Comment: 8 pages, 2 figures, figures have been updated and PACS numbers have been added, text have been updated with enhanced contents and reference

Conservation Law for Massive Scale-Invariant Photons in Weyl-Invariant Gravity

It is demonstrated that a Stueckelberg-type gauge theory, coupled to the scalar-tensor theory of gravity, is invariant under both gauge and Weyl transformations. Unlike the pure Stueckelberg theory, this coupled Lagrangian has a genuine Weyl symmetry, with a non-vanishing current. The above is true in the Jordan frame, whereas in the Einstein frame, the same theory manifests as Proca theory in presence of pure gravity. It is found that broken scale invariance leads to simultaneous spontaneous breaking of the gauge symmetry.Comment: 11 pages, title modified, minor corrections, typos fixed, references updated, no figure

Use of Posterior Hamstring Harvest During Anterior Cruciate Ligament Reconstruction in the Pediatric and Adolescent Population.

Background:Posterior hamstring harvest has been described in the adult population in a limited fashion, but no study is available describing the use of posterior hamstring harvest in an active pediatric and adolescent cohort. At times, surgeons may be faced with a challenging anterior harvest due to patient anatomic characteristics, particularly the anatomic features and size of the pes tendons. Clinicians need to have multiple harvest approaches at their disposal. Complications with hamstring harvest such as premature graft transection are more problematic in this population due to higher failure rates with allograft tissue. The posterior harvest via its more proximal location may allow for easier tendon identification, visualization of the accessory attachments, and longer preserved tendon length if transection error occurs when the anterior approach is avoided based on surgical technique, patient anatomic characteristics, and surgeon and patient preference. Purpose:To describe the technique of a posterior hamstring harvest in pediatric and adolescent patients and to analyze complications. Study Design:Case series; Level of evidence, 4. Methods:This study was a retrospective review of a consecutive series of pediatric and adolescent patients who underwent posterior hamstring harvest. During surgery, the patient's leg was abducted and externally rotated to expose the posteromedial aspect of the knee. A 2-cm incision was made overlying the palpable medial hamstring at the popliteal crease. The posterior hamstring tendons were first harvested proximally with an open tendon stripper and distally with a closed stripper. Preoperative, intraoperative, and postoperative findings and complications were analyzed. Results:A total of 214 patients (mean ± SD age, 15.7 ± 4.1 years; range, 8.0-19.8 years) underwent posterior harvest, with a mean ± SD follow-up of 1.83 ± 1.05 years. No complications occurred in our series related to graft harvest-no graft transections, neurovascular injuries, secondary procedures for wound healing or closure, cosmetic concerns, or limitations in return to activity due to the posterior incision. Conclusion:The posterior hamstring harvest is a safe and reliable technique to harvest autograft tendon in pediatric and adolescent anterior cruciate ligament reconstructions. The posterior technique entailed no complications related to harvest. No patients expressed any cosmetic concerns about their incision or had limitations in return to sport due to the posterior harvest