Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects

This article extends our previous analysis Stránský et al. (2014) of Excited-State Quantum Phase Transitions (ESQPTs) in systems of dimension two. We focus on the oscillatory component of the quantum state density in connection with ESQPT structures accompanying a first-order ground-state transition. It is shown that a separable (integrable) system can develop rather strong finite-size precursors of ESQPT expressed as singularities in the oscillatory component of the state density. The singularities originate in effectively 1-dimensional dynamics and in some cases appear in multiple replicas with increasing excitation energy. Using a specific model example, we demonstrate that these precursors are rather resistant to proliferation of chaotic dynamics.     

共形空间${\mathbb Q}^n_s$中的正则Blaschke拟全脐子流形

[Nie C X,Wu C X,Regular submanifolds in the conformal space Q_p~n,ChinAnn Math,2012,33B(5):695-714]中研究了共形空间Q_s~n中的正则子流形,并引入了共形空间Q_s~n中的子流形理论.本文作者将分类共形空间Q_s~n中的Blaschke拟全脐子流形,证明伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形是共形空间中的Blaschke拟全脐子流形;反之,共形空间中的Blaschke拟全脐子流形共形等价于伪Riemann空间形式中具有常数量曲率和平行的平均曲率向量场的正则子流形.这一结论可看作是共形空间Q_s~n中共形迷向子流形分类定理的推广.     

About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers

We first globalize some recent results about polynomials whose divided differences are integer-valued on subsets of discrete valuation domains. This allows us to describe explicit computations, in particular for polynomials which are integer-valued on the prime numbers. Then, we specialize other recent results about integer-valued polynomials on triangular matrices to matrices whose coefficients are in some subsets, and in particular, when the coefficients are primes.     

The transport equation in the scaling invariant Besov or Essén–Janson–Peng–Xiao space

This paper addresses a well-posedness of the weak solution to the transport equation (describing how a scalar quantity is transported in a space) with an initial data in the scaling invariant Besov or Essén–Janson–Peng–Xiao space via the boundedness of the left and right compositions acting on each space.     

Analysis of solid solutions stability in scheelite-type molybdates and tungstates

Mutual solubility of bivalent metal molybdates and tungstates with scheelite structure was theoretically estimated by calculating formation enthalpies and the maximal decomposition temperatures of solid solutions at different temperatures. The theoretical stability of continuous solid solutions in binary systems of bivalent metal molybdates and tungstates was found to be higher than reported literature data. After cooling down continuous substitution solid solution should remain in following systems: CaMoО₄–CdMoО₄, SrMoО₄–MMoО₄ (M=Ba, Pb), BaMoО₄–PbMoО₄, SrWO₄–MWO₄ (M=Ca, Pb), and BaWO₄–PbWO₄. There is a probability that at room temperature in systems CaMoО₄–SrMoО_4, CaWO₄–PbWO₄, and BaWO₄–SrWO₄ the single homogeneity region may decompose to limited solid solutions. It was shown experimentally that a continuous series of scheelite-structure solid solutions M_1−xM^I_xТO₄ can be formed via citrate synthesis at temperatures below 500°С.     

Reversal of myo-inositol metabolic level in the left dorsolateral prefrontal cortex of rats exposed to forced swimming test following desipramine treatment: an in vivo localized H-MRS study at 4.7 T

The forced swimming test (FST) is a useful paradigm that is relatively quick and simple to perform and has been utilized to predict antidepressant activity based on learned helplessness as a model of depression. To date, few studies have used proton magnetic resonance spectroscopy (¹H-MRS) to assess antidepressant effects in rats. The purpose of this study was to assess desipramine (DMI) effects on the left dorsolateral prefrontal cortex (DLPFC) of the rats, which were randomly assigned to three groups (control, n=10; FST+saline, n=10; FST+DMI, n=10), using single-voxel localization technique. All ¹H-MRS experiments were performed on a Bruker 4.7-T scanner with 400 mm bore magnet, allowing for acquisition of in vivo ¹H point-resolved spectroscopy spectra (TR/TE=3000/30 ms, number of data points=2048, NEX=512, voxel volume=27 μl, scan time=25 min). Proton metabolites were quantified automatically using LCModel software and were expressed as ratios to total creatine (Cr+PCr). Major target metabolites such as N-acetyl aspartate (NAA)+N-acetylaspartylglutamate (NAAG), glutamate+glutamine (Glu+Gln), glycerophosphorylcholine+phosphorylcholine (GPC+PCho), myo-inositol (mIns) and taurine (Tau) were successfully quantified with Cramer–Rao lower boundary ≤10%. There were significantly higher mIns/(Cr+PCr) and mIns/(NAA+NAAG) ratios in the FST+saline group compared to the control group. In the FST+DMI group, both mIns/(Cr+PCr) and mIns/(NAA+NAAG) ratios were significantly decreased to the level similar to those in the control group. No other metabolite ratios were significantly different among the three groups. Our findings suggest a possible role of altered mIns level within the left DLPFC of the rat model for depression.     

Singular Hartree equation in fractional perturbed Sobolev spaces

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.     

正六边形自聚焦透镜折射率分布研究

针对离子交换实验的定源扩散,提出了一种求解正六边形自聚焦透镜折射率分布的理论模型.并在此基础上采用分离变量法和坐标变换,求得了正六边形自聚焦透镜折射率分布的解析解.通过Matlab对该解析解进行了模拟比较,定性、定量地证明了其正确性.     

拟连续Domain的若干拓扑性质

对拟连续Domain D证明了:(1)双拓扑空间(D,σ(D),(D))为两两完全正则空间;(2)若D有可数基,则(max(D),σ(D)max(D))为正则空间当且仅当它为Polish空间;(3)拓扑空间(D,σb(D))为零维Tychonoff空间,其中σb(D)为D上Scott拓扑的b-拓扑。     

Cohomology,extensions and automorphisms of skew braces

The second cohomology group of a left skew brace with coefficients in a trivial left brace with non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial brace is established and a Wells' like exact sequence relating the second cohomology group with inducible automorphisms of an extension of left skew braces is constructed.