Ground state properties of a Tonks-Girardeau Gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.Comment: 9 pages, 10 figure

Passive faraday mirror attack in practical two-way quantum key distribution system

The faraday mirror (FM) plays a very important role in maintaining the stability of two way plug-and-play quantum key distribution (QKD) system. However, the practical FM is imperfect, which will not only introduce additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper, we propose a passive faraday mirror attack in two way QKD system based on the imperfection of FM. Our analysis shows that, if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish these states with a set of POVM operators belonging to three dimension space, which will reduce the QBER induced by her attack. Furthermore, a relationship between the degree of the imperfection of FM and the transmittance of the practical QKD system is obtained. The results show that, the probability that Eve loads her attack successfully depends on the degree of the imperfection of FM rapidly, but the QBER induced by Eve's attack changes with the degree of the imperfection of FM slightly

Possible Superconductivity at 37 K in Graphite-Sulfur Composite

Sulfur intercalated graphite composites with diamagnetic transitions at 6.7 K and 37 K are prepared. The magnetization hysteresis loops (MHL), Xray diffraction patterns, and resistance were measured. From the MHL, a slight superconducting like penetration process is observed at 15 K in low field region. The XRD shows no big difference from the mixture of graphite and sulfur indicating that the volume of the superconducting phase (if any) is very small. The temperature dependence of resistance shows a typical semiconducting behavior with a saturation in low temperature region. This saturation is either induced by the de-localization of conducting electrons or by possible superconductivity in this system.Comment: CHIN. PHYS.LETT v18 1648 (2001

A New Kind of Shift Operators for Infinite Circular and Spherical Wells

A new kind of shift operators for infinite circular and spherical wells is identified. These shift operators depend on all spatial variables of quantum systems and connect some eigenstates of confined systems of different radii R sharing energy levels with a common eigenvalue. In circular well, the momentum operators P±=Px±iPy play the role of shift operators. The Px and Py operators, the third projection of the orbital angular momentum operator Lz, and the Hamiltonian H form a complete set of commuting operators with the SO(2) symmetry. In spherical well, the shift operators establish a novel relation between ψlm(r) and ψ(l ± 1)(m±1)(r)

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

Strong quantum fluctuation of vortices in the new superconductor MgB2MgB_2

By using transport and magnetic measurement, the upper critical field $H_{c2}(T)$ and the irreversibility line $H_{irr}(T)$ has been determined. A big separation between $H_{c2}(0)$ and $H_{irr}(0)$ has been found showing the existence of a quantum vortex liquid state induced by quantum fluctuation of vortices in the new superconductor $MgB_2$. Further investigation on the magnetic relaxation shows that both the quantum tunneling and the thermally activated flux creep weakly depends on temperature. But when the melting field $H_{irr}$ is approached, a drastic rising of the relaxation rate is observed. This may imply that the melting of the vortex matter at a finite temperature is also induced by the quantum fluctuation of vortices.Comment: 4 pages, 4 figure

Production of the neutral top-pion πt0\pi_{t}^{0} in association with a high-pTp_{T} jet at the LHCLHC

In the framework of the topcolor-assisted technicolor $(TC2)$ model, we study production of the neutral top-pion $\pi_{t}^{0}$ in association with a high-$p_{T}$ jet at the $LHC$, which proceeds via the partonic processes $gg\longrightarrow \pi_{t}^{0}g$, $gq\longrightarrow \pi_{t}^{0}q$, $q\bar{q}\longrightarrow \pi_{t}^{0}g$, $gb(\bar{b})\longrightarrow \pi_{t}^{0}b(\bar{b})$, and $b\bar{b}\longrightarrow \pi_{t}^{0}g$. We find that it is very challenging to detect the neutral top-pion $\pi_{t}^{0}$ via the process $pp\longrightarrow \pi_{t}^{0}+jet+X\to t\bar{t}+jet+X$, while the possible signatures of $\pi_{t}^{0}$ might be detected via the process $pp\longrightarrow \pi_{t}^{0}+jet+X\to(\bar{t}c+t\bar{c})+jet+X$ at the $LHC$.Comment: 13 pages, 4 figures; typos correcte

Universal role of correlation entropy in critical phenomena

In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.Comment: 10 pages, 9 figure

Smart Machine Vision for Universal Spatial Mode Reconstruction

Structured light beams, in particular those carrying orbital angular momentum (OAM), have gained a lot of attention due to their potential for enlarging the transmission capabilities of communication systems. However, the use of OAM-carrying light in communications faces two major problems, namely distortions introduced during propagation in disordered media, such as the atmosphere or optical fibers, and the large divergence that high-order OAM modes experience. While the use of non-orthogonal modes may offer a way to circumvent the divergence of high-order OAM fields, artificial intelligence (AI) algorithms have shown promise for solving the mode-distortion issue. Unfortunately, current AI-based algorithms make use of large-amount data-handling protocols that generally lead to large processing time and high power consumption. Here we show that a low-power, low-cost image sensor can itself act as an artificial neural network that simultaneously detects and reconstructs distorted OAM-carrying beams. We demonstrate the capabilities of our device by reconstructing (with a 95$\%$ efficiency) individual Vortex, Laguerre-Gaussian (LG) and Bessel modes, as well as hybrid (non-orthogonal) coherent superpositions of such modes. Our work provides a potentially useful basis for the development of low-power-consumption, light-based communication devices