Letter: Global Hyperbolicity of Sliced Spaces

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.     

面向脉冲量子级联激光器气体检测的锁相放大器

为了在基于脉冲式中红外量子级联激光器的气体检测系统中,精确提取窄脉冲传感信号的幅度,设计并实现了一种微秒级窄脉冲锁相放大器.根据微秒级窄脉冲的特点,窄脉冲信号经过窄带通滤波电路,得到基频正弦波信号,再经过主放大、移相、相敏检波电路,得到与脉冲幅值有关的直流信号.利用信号发生器产生的幅度、频率、相位可调的窄脉冲待测信号,对锁相放大器进行功能验证实验.结果表明,锁相放大器输出直流信号与输入信号的幅度呈良好的线性关系,线性拟合度约为98.043%;信号幅值的相对测量误差不超过3%;在1 h的测试时间内,信号波动范围在1‰以内.利用配备的不同浓度的一氧化碳样品及研制的锁相放大器,开展了一氧化碳气体检测实验.在0~180 ppm范围内,随着一氧化碳浓度的增加,锁相放大器的输出电压值与一氧化碳浓度呈现良好的e指数关系.根据A11an方差预测的系统检测下限为0.4123ppm.与商用锁相放大器相比,该放大器具有体积小、成本低、易于集成等特点,在基于脉冲式中红外量子级联激光器的气体检测中具有较好的应用前景.     

Letter: On the Global Hyperbolicity of Lorentz 2-Step Nilpotent Lie Groups

This work is concerned with the existence of Lorentz 2-step nilpotent Lie groups having a timelike center and which are not globally hyperbolic. Namely, we prove that any left invariant Lorentz metric with a timelike center on the Heisenberg group H ²ⁿ⁺¹ is not globally hyperbolic.     

Two-Dimensional Quantum Gas

Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats.     

Global Completability with Applications to Self-Consistent Quantum Tomography

Motivated by recent developments on solvable directed polymer models, we define a ‘multi-layer’ extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture.     

Hyperbolicity conditions for the Lorenz model

It was shown earlier by Bunimovich and Sinai that the Lorenz Model has a natural invariant measure if the so-called hyperbolicity conditions hold. In this paper we represent results of a numerical verification of the hyperbolicity conditions for the Lorenz model with the values of the parameters $\text{б = 6}$, r = 28, $\text{b =}\text{8}\text{3}$.     

Boundary Problems for the Quantum Bose Gas

A relaxation kinetic equation that describes the behavior of a Bose gas is derived. The Kramers half-space problem on isothermal slip is treated. An analytical solution and the number-of-particle distribution function for particles flying toward a wall, in explicit form, are obtained. The dependence of the slip velocity on the parameter that is the ratio of the chemical potential to the product of Boltzmann's constant by the absolute temperature is analyzed. The influence of the quantum effects on the isothermal slip coefficient is evaluated for He⁴.     

Quantum Entropy of Black Hole with Internal Global Monopole

Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.     

Global Positioning Scheme via Quantum Teleportation

Quantum teleportation scheme is undoubtedly an inspiring theoretical discovery as an amazing application of quantum physics, which was experimentally realized several years later. For the purpose of quantum communication via this scheme, an entangled ancillary pair shared by Alice and Bob is the essential ingredient, and a quantum memory in Bob’s system is necessary for him to keep the quantum state until the classical message from Alice arrives. Yet, the quantum memory remains a challenge in bo...     

The Boltzmann Equation for a One-Dimensional Quantum Lorentz Gas

We study the macroscopic behavior of a quantum particle under the action of randomly distributed scatterers on the real line. Each scatterer generates a δ-potential. We prove that, in the low density limit, the Wigner function of the system converges to a probability distribution satisfying a classical linear Boltzmann equation, with a scattering cross section computed according to the Quantum Mechanical rules. Received: 2 April 1998 / Accepted: 12 February 1999     

On a Quantum System with Memory

We consider the integro-differential equation for the classical trajectory of an oscillator coupled to another one. On the quantum level the elimination of the coordinate A of the “unvisible” oscillator leads to an effective path integral (X, Ξ, μ) for the associated imaginary time stochastic process t ?, (-∞,∞) → x(t). We prove reflection positivity of the measure dμ ≈ F · dξ, where dξ governes the free oscillator x and F is the counterpart of Feynman's influence functional. Finally, realizing the Hamiltonian semigroup exp(-tH), t ≧ 0, in the physical Hilbert space ?? = L²(X, Γ, μ), where Γ ? Ξ₊, we try to understand what is memory.     

One-Loop Quantum Corrections to Thermodynamics of Black Holes with Global Monopoles

Quantum corrections are studied for a black holewith a global monopole charge in a 2D model obtained byspherisymmetric reduction of the 4D action. Thebackreaction of the Hawking radiation on the geometry is studied perturbatively for conformal matter.It is shown that the metric and the position of horizonchange by an amount of order . Within theoff-shell approach the one-loop thermodynamicquantities, energy, and entropy are found. They are shownto contain two parts, one due to the hole itself and oneto the hot gas surrounding it. The deviation of thequantum-corrected entropy from the classical one is given.     

Non-Stationary Non-Uniform Hyperbolicity: SRB Measures for Dissipative Maps

We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an “effective hyperbolicity” condition that guarantees certain recurrence conditions on the iterates of Lebesgue measure. We give examples of systems that do not admit a dominated splitting but can be shown to have SRB measures using our methods.     

Global Regularity for the Navier-Stokes-Maxwell System with Fractional Diffusion

In this paper, we study the global regularity for the Navier-Stokes-Maxwell system with fractional diffusion. Existence and uniqueness of global strong solution are proved for \(\alpha \geqslant \frac {3}{2}\). When 0 < α < 1, global existence is obtained provided that the initial data \(\|u_{0}\|_{H^{\frac {5}{2}-2\alpha }}+\|E_{0}\|_{H^{\frac {5}{2}-2\alpha }}+\|B_{0}\|_{H^{\frac {5}{2}-2\alpha }}\) is sufficiently small. Moreover, when \(1<\alpha <\frac {3}{2}\), global existence is obtained if for any ε >?0, the initial data \(\|u_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}+\|E_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}+\|B_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}\) is small enough.     

Quantum Statistics for General Quadratic System

By the generalized linear quantum transformation theory, we concisely derive the analytic expressions of partition function for general quadratic systems of multi-mode boson and fermion Fock space without any information for the energy spectrum. Under a general condition, we firstly acquire the exact expressions of energy spectra for these systems.     

A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows

In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥?2. We prove that there exists a C²-residual subset \(\mathscr{R}\) of metrics on a given compact Riemannian manifold such that if \(g\in \mathscr{R}\), then its associated geodesic flow \({\varphi ^{t}_{g}}\) is expansive if and only if the closure of the set of periodic orbits of \({\varphi ^{t}_{g}}\) is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C²-residual \(\mathscr{R}\) such that if \(g\in \mathscr{R}\), then its associated geodesic flow \({\varphi ^{t}_{g}}\) is expansive if and only if \({\varphi ^{t}_{g}}\) is an Anosov flow.     

量子效应对液体水结构的影响

利用高灵敏的拉曼光谱系统地研究了由量子效应引起的轻水和重水的结构差异. 测量了5～85 oC的轻水和重水的拉曼光谱,明显地观察到两种水的拉曼光谱谱形的差别. 使用全局拟合方法分析了所有谱图的谱形,结果显示在同一个温度下重水的局部结构要比轻水的结构有序,并且他们结构上的差异随着温度的升高而减少. 另外计算了水结构差异的指标|温度漂移,从低温到高温时这个指标从28 oC减小到18 oC. 这些结构差异表明量子效应在室温范围内也非常重要. 我们还利用Vant't Hoff关系式分析了水分子相互作用能. 这些结构上的细节可以帮助建立更加可靠的水模型.     

Geometric Global Quantum Discord of Two-qubit X States

In this paper, we find that the geometric global quantum discord proposed by Xu and the total quantum correlations proposed by Hassan and Joag are identical. Moreover, we work out the analytical formulas of the geometric global quantum discord and geometric quantum discord both for two-qubit X states, respectively. We further illustrate how to use these formulas to deal with a few particular examples. We also compare the results achieved by using three kinds of geometric quantum discords. The geometric quantum discord is verified as a tight lower bound of the geometric global quantum discord for two-qubit X states.     

Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials

We consider a quantum particle interacting with N obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form N²V (Nx) (Gross-Pitaevskii potential). We show convergence of the N dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our Lorentz gas model exhibits a universal behavior for N large. Moreover we explicitely characterize the fluctuations around the limit operator. Our model can be considered as a simplified model for scattering of slow neutrons from condensed matter.