Transition from non-fermi liquid behavior to Landau–Fermi liquid behavior induced by magnetic fields

We show that a strongly correlated Fermi system with a fermion condensate which exhibits strong deviations from Landau–Fermi liquid behavior is driven into the Landau–Fermi liquid by applying a small magnetic field B at temperature T=0. This field-induced Landau–Fermi liquid behavior provides constancy of the Kadowaki–Woods ratio. A re-entrance into the strongly correlated regime is observed if the magnetic field B decreases to zero; the effective mass M* then diverges as \(M^* \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\). At finite temperatures, the strongly correlated regime is restored at some temperature \(T^* \propto \sqrt B \). This behavior is of a general form and takes place in both three-dimensional and two-dimensional strongly correlated systems. We demonstrate that the observed \({1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}\) divergence of the effective mass and other specific features of heavy-fermion metals are accounted for by our consideration.     

Linewidth of a quantum-cascade laser assessed from its frequency noise spectrum and impact of the current driver

We report on the measurement of the frequency noise properties of a 4.6-??m distributed-feedback quantum-cascade laser (QCL) operating in continuous wave near room temperature using a spectroscopic set-up. The flank of the R(14) ro-vibrational absorption line of carbon monoxide at 2196.6?cm^?1 is used to convert the frequency fluctuations of the laser into intensity fluctuations that are spectrally analyzed. We evaluate the influence of the laser driver on the observed QCL frequency noise and show how only a low-noise driver with a current noise density below ${\approx} 1~\mbox{nA/}\sqrt{}\mbox{Hz}$ allows observing the frequency noise of the laser itself, without any degradation induced by the current source. We also show how the laser FWHM linewidth, extracted from the frequency noise spectrum using a simple formula, can be drastically broadened at a rate of ${\approx} 1.6~\mbox{MHz/}(\mbox{nA/}\sqrt{}\mbox{Hz})$ for higher current noise densities of the driver. The current noise of commercial QCL drivers can reach several $\mbox{nA/}\sqrt{}\mbox{Hz}$ , leading to a broadening of the linewidth of our QCL of up to several megahertz. To remedy this limitation, we present a low-noise QCL driver with only $350~\mbox{pA/}\sqrt{}\mbox{Hz}$ current noise, which is suitable to observe the ??550?kHz linewidth of our QCL.     

Long-Time Asymptotics for the Focusing NLS Equation with Time-Periodic Boundary Condition on the Half-Line

We consider the focusing nonlinear Schrödinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time- periodic, of the form \({a{\rm e}^{\i\alpha} {\rm e}^{2\i\omega t}}\) . The goal of this paper is to study the asymptotic behavior of the solution of this initial-boundary-value problem. The main tool is the asymptotic analysis of an associated matrix Riemann–Hilbert problem. We show that for \({\omega < -3a^2}\) the solution of the IBV problem has different asymptotic behaviors in different regions. In the region \({x > 4bt}\) , where \({b\mathop{:=} \sqrt{(a^2-\omega)/2} > 0}\) , the solution takes the form of the Zakharov-Manakov vanishing asymptotics. In a region of type \({4bt-\frac{N+1}{2a} {\rm log} t < x < 4bt}\) , where N is any integer, the solution is asymptotic to a train of asymptotic solitons. In the region \({4(b-a\sqrt2)t < x < 4bt}\) , the solution takes the form of a modulated elliptic wave. In the region \({0 < x < 4(b-a\sqrt2)t}\) , the solution takes the form of a plane wave.     

Quantum Entanglement Under Lorentz Transformation

We study the properties of quantum entanglement in moving frames, with a non-maximally entangled bipartite state: $|\phi\rangle=\sqrt{1-\varepsilon}|{\uparrow\uparrow}\rangle +\sqrt{\varepsilon}|{\downarrow\downarrow}\rangle$ , (0<ε<1). We calculate the concurrence of this state under Lorentz transformation and show that if the momenta part of the spin-1/2 pair is appropriately correlated, the concurrence is invariant ( $\mathcal {C}(\rho)=2\sqrt{\varepsilon-\varepsilon^{2}}$ ); despite the entanglement of this state is not maximal, there is no transfer of entanglement between spin and momentum.     

Fully constrained Majorana neutrino mass matrices using $$\varvec{\varSigma (72\times 3)}$$

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (\(\nu _2\)) columns, namely tri-chi-maximal mixing (\(\text {T}\chi \text {M}\)) and tri-phi-maximal mixing (\(\text {T}\phi \text {M}\)), were proposed. In 2012, it was shown that \(\text {T}\chi \text {M}\) with \(\chi =\pm \,\frac{\pi }{16}\) as well as \(\text {T}\phi \text {M}\) with \(\phi = \pm \,\frac{\pi }{16}\) leads to the solution, \(\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}\), consistent with the latest measurements of the reactor mixing angle, \(\theta _{13}\). To obtain \(\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}\) and \(\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}\), the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, \(m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}\). In this paper we construct a flavour model based on the discrete group \(\varSigma (72\times 3)\) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric \(3\times 3\) matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of \(\varSigma (72\times 3)\). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.     

On quantum analogue of dynamical stabilisation of inverted harmonic oscillator by time periodical uniform field

Quantum analogue of stabilised forced oscillations around an unstable equilibrium position is explored by solving the non-stationary Schrödinger equation (NSE) of the inverted harmonic oscillator (IHO) driven periodically by spatial uniform field of frequency \(\Omega \), amplitude \(F_{0}\) and phase \(\phi \), i.e. the system with the Hamiltonian of \(\hat{{H}}=(\hat{{p}}^{2}/2m)-(m\omega ^{2}x^{2}/2)-F_0 x\sin \) \(\left( {\Omega t+\phi } \right) \). The NSE has been solved both analytically and numerically by Maple 15 in dimensionless variables \(\xi = x\sqrt{m\omega /\hbar }\hbox {, }f_0 =F_0 /\omega \sqrt{\hbar m\omega }\) and \(\tau =\omega t\). The initial condition (IC) has been specified by the wave function (w.f.) of a generalised Gaussian type which suits well the corresponding quantum IC operator. The solution obtained demonstrates the non-monotonous behaviour of the coordinate spreading \(\sigma \left( \tau \right) \hbox { =}\sqrt{\big ( {\overline{\Delta \xi ^{2}\big ( \tau \big )} } \big )}\) which decreases first from quite macroscopic values of \(\sigma _{0} =2^{12,\ldots ,25}\) to minimal one of \(\sim \!(1/\sqrt{2})\) at times \(\tau <\tau _0 =0.125\ln \!\left( {16\sigma _0^4 +1} \right) \) and then grows back unlimitedly. For certain phases \(\phi \) depending on the \(\Omega /\omega \) ratio and \(n=\log _2\!\sigma _0 \), the mass centre of the packet \(\xi _{\mathrm {av}}( \tau )= \overline{\hat{{x}}(\tau )} \cdot \sqrt{m\omega /\hbar }\) delays approximately two natural ‘periods’ \(\sim \!(4\pi /\omega )\) in the area of the stationary point and then escapes to ‘\(+\)’ or ‘?’ infinity in a bifurcating way.  For ‘resonant’ \(\Omega =\omega \), the bifurcation phases \(\phi \) fit well with the regression formula of Fermi–Dirac type of argument n with their asymptotic \(\phi ( {\Omega ,n\rightarrow \infty } )\) obeying the classical formula \(\phi _{\mathrm {cl}} ( \Omega )=-\hbox {arctg} \, \Omega \) for initial energy \(E = 0\) in the wide range of \(\Omega =2^{-4},...,2^{7}\).     

Superconductive superheating field for finiteκ

We have calculated analytically the superheating fieldH _sh for bulk superconductors, correct to second order in. We find , which agrees well with numerical computations for<0.5. The surface order parameter is , and the penetration depth is .     

Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction

The uniqueness and the global Markov property for the regular Gibbs measure corresponding to the interaction $$U_\Lambda (\varphi ): = \lambda \int\limits_\Lambda {d_2 x\int {d\varrho (\alpha ):e^{\alpha \varphi } :_0 (x)} } $$ [forλ>0,d?(α) a probability measure with support in \(( - 2\sqrt {\pi ,} 2\sqrt \pi )\) ] is proved.     

On Essential Self-Adjointness for Magnetic Schrödinger and Pauli Operators on the Unit Disc in $${\mathbb {R}^2}$$

We study the question of magnetic confinement of quantum particles on the unit disk \({\mathbb {D}}\) in \({\mathbb {R}^2}\) , i.e. we wish to achieve confinement solely by means of the growth of the magnetic field \({B(\vec x)}\) near the boundary of the disk. In the spinless case, we show that \({B(\vec x)\ge \frac{\sqrt 3}{2}\cdot\frac{1}{(1-r)^2}-\frac{1}{\sqrt 3}\frac{1}{(1-r)^2\ln \frac{1}{1-r}}}\) , for \({|\vec x|}\) close to 1, insures the confinement provided we assume that the non-radially symmetric part of the magnetic field is not very singular near the boundary. Both constants \({\frac{\sqrt 3}{2}}\) and \({-\frac{1}{\sqrt 3}}\) are optimal. This answers, in this context, an open question from Colin de Verdière and Truc (Ann Inst Fourier 2011, Preprint, arXiv:0903.0803v3). We also derive growth conditions for radially symmetric magnetic fields which lead to confinement of spin 1/2 particles.     

Boson-fermion Holstein-Primakoff mapping at nonzero temperatures for the example of the Lipkin model

Within the formalism of thermo field dynamics, the boson-fermion Holstein-Primakoff transformation is constructed for the case of nonzero temperatures. For the example of the Lipkin model, the transformation in question is used to construct a thermal Hamiltonian in the form of an expansion in the parameter \({1 \mathord{\left/ {\vphantom {1 {\sqrt N }}} \right. \kern-\nulldelimiterspace} {\sqrt N }}\), where N is the number of particles in the system. The temperature dependence of quasiparticle (fermion) and collective-excitation (boson) energies is calculated to terms of order 1/N.     

Scalar electron and zino production on and beyond theZ resonance ine + e − annihilation

We study the production of scalar electrons ine ⁺ e ^? collisions on and above theZ resonance. By calculating the cross-section for \(e^ + e^ - \to e^ + e^ - \tilde \gamma \tilde \gamma \) we show that scalar electrons with mass above the beam energies \((\sqrt s /2)\) can be identified. In particular if a zino with mass \(m_{\tilde z}< \sqrt s - m_{\tilde \gamma } \) exists then zino production and decay can give a contribution which dominates the γ exchange contributions. We present final state distributions.     

The Scaling Limit of the Critical One-Dimensional Random Schrödinger Operator

We consider two models of one-dimensional discrete random Schrödinger operators

$(H_n\psi)_\ell =\psi_{\ell -1}+\psi_{\ell +1}+v_\ell \psi_\ell$

, \({\psi_0=\psi_{n+1}=0}\) in the cases \({ v_k=\sigma \omega_k/\sqrt{n}}\) and \({ v_k=\sigma \omega_k/ \sqrt{k}}\) . Here ω _k are independent random variables with mean 0 and variance 1.

We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem.In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the β-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.     

Dynamical Localization for the Random Dimer Schrödinger Operator

We study the one-dimensional random dimer model, with Hamiltonian H _ω =Δ+V _ω , where for all x∈ $\mathbb{Z}$ , V _ω(2x)=V _ω(2x+1) and where the V _ω(2x) are i.i.d. Bernoulli random variables taking the values ±V, V>0. We show that, for all values of Vand with probability one in ω, the spectrum of His pure point. If V≤1 and V≠1/ $\sqrt 2$ , the Lyapunov exponent vanishes only at the two critical energies given by E=±V. For the particular value V=1/ $\sqrt 2$ , respectively, V= $\sqrt 2$ , we show the existence of new additional critical energies at E=±3/ $\sqrt 2$ , respectively, E=0. On any compact interval Inot containing the critical energies, the eigenfunctions are then shown to be semi-uniformly exponentially localized, and this implies dynamical localization: for all q>0 and for all ψ∈ $\ell$ ²( $\mathbb{Z}$ ) with sufficiently rapid decrease $${\mathop {\sup }\limits_t} r_{\psi ,I}^{\left( q \right)} {\kern 1pt} \left( t \right): = {\mathop {\sup }\limits_t} \left\langle {P_I \left( {H\omega } \right)\psi _t ,\left| X \right|^q P_I \left( {H\omega } \right)\psi _t } \right\rangle < \infty $$ Here $\psi _t = e^{- iH_{\omega ^t}} \psi$ , and P _I(H _ω) is the spectral projector of H _ωonto the interval I. In particular, if V>1 and V≠ $\sqrt 2$ , these results hold on the entire spectrum [so that one can take I=σ(H _ω)].     

Formation of a narrow baryon resonance with positive strangeness in K + collisions with Xe nuclei

The data on the charge-exchange reaction K ⁺Xe → K ⁰ pXe′, obtained with the bubble chamber DIANA, are reanalyzed using increased statistics and updated selections. Our previous evidence for formation of a narrow pK ⁰ resonance with mass near 1538 MeV is confirmed. The statistical significance of the signal reaches some 8 (6) standard deviations when estimated as $ {S \mathord{\left/ {\vphantom {S {\sqrt B \left( {{S \mathord{\left/ {\vphantom {S {\sqrt {B + S} }}} \right. \kern-0em} {\sqrt {B + S} }}} \right)}}} \right. \kern-0em} {\sqrt B \left( {{S \mathord{\left/ {\vphantom {S {\sqrt {B + S} }}} \right. \kern-0em} {\sqrt {B + S} }}} \right)}} $ . The mass and intrinsic width of the Θ⁺ baryon are measured as m = 1538 ± 2 MeV and Γ = 0.39 ± 0.10 MeV.     

On Conformal Field Theory of SLE(κ,ρ)

SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-L?wner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = . The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(κ ρ)     

Evolution Law of the Optical Field of Degenerate Parametric Amplifier in Dissipative Channel

We explore the time-evolution law of the optical field of degenerate parametric amplifier (DPA) in dissipative channel. It turns out that its density operator at initial time ρ ₀ = A exp(E ^? a ^?2) exp(a ^? alnλ) exp(E a ²) evolves into \(\rho (t)= \frac {A}{\lambda ^{\prime }}\) \(\exp \left (\frac {E^{\ast }e^{-2\kappa t}a^{\dag 2}}{ \lambda ^{\prime 2}}\right )\exp \left \{a^{\dag }a\ln \frac {[\lambda -(\lambda ^{2}-4|E|^{2})T]e^{-2\kappa t}}{\lambda ^{\prime 2}}\right \} \exp \left (\frac { Ee^{-2\kappa t}a^{2}}{\lambda ^{\prime 2}}\right ),\) where κ is the damping constant of the channel, T = 1 ? e ^?2κt , and \(\lambda ^{\prime }\equiv \sqrt {(1-\lambda T)^{2}-4|E|^{2}T^{2}}.\) We employ the method of integration (or summation) within an ordered (normally ordered or antinormally ordered) of operators to overcome the obstacles in the process of calculation.     

O(G μ 2 m t 4 ) electroweak radiative corrections to theZb \bar b vertex

The leading heavy-top two-loop corrections to theZb \(\bar b\) vertex are determined from a direct evaluation of the corresponding Feynman diagrams in the largem _t limit. The leading one-loop top-mass effect is enhanced by \([{{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} \mathord{\left/ {\vphantom {{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} {(8\pi ^2 \sqrt 2 )}}} \right. \kern-0em} {(8\pi ^2 \sqrt 2 )}}]\) . Our calculation confirms a recent result of Barbieri et al..     

The BCS Critical Temperature for Potentials with Negative Scattering Length

We prove that the critical temperature for the BCS gap equation is given by ${T_c = \mu \left( \frac 8\pi {\rm e}^{\gamma -2} + o(1) \right) {\rm e}^{\pi/(2\sqrt \mu a)}}$ in the low density limit μ→ 0, with γ denoting Euler’s constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.     

The Essence of Operators’ Weyl Ordering Scheme and New Operator Identities for Converting Q−P Ordering to Weyl Ordering

We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H _m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively.     

Trajectories in Random Monads

Let us have a non-empty finite set S with n>1 elements which we call points and a map M:S→S. After V.I. Arnold, we call such pairs (S, M) monads, but we consider random monads in which all the values of M(?) are random, independent and uniformly distributed in S. We fix some ⊙∈S and consider the infinite sequence M ^t (⊙), t=0,1,2,…?. A point is called visited if it coincides with at least one term of this sequence. A visited point is called recurrent if it appears in this sequence at least twice; if a visited point appears in this sequence only once, it is called transient. We denote by Vis, Rec, Tra the numbers of visited, recurrent and transient points respectively and study their distributions. The distributions of Vis, Rec, Tra are unimodal. The modes of Rec and Tra equal their minimal values, that is 1 and 0 respectively. The mode of Vis is approximated by \(\sqrt{n}\), plus-minus a constant. The mathematical expectations: \(\mathbb{E}(\mathit{Vis})\) is approximated by \(2 \sqrt{\pi\, n/8}\) plus-minus a constant; \(\mathbb{E}(\mathit{Rec})\) and \(\mathbb{E}(\mathit{Tra})\) are approximated by \(\sqrt{\pi\, n/8}\) plus-minus a constant. For the standard deviations σ(Vis) and σ(Rec)=σ(Tra) respectively we present the approximations

$\sqrt{\frac{4-\pi}{2} \cdot n} \quad\mbox{and}\quad \sqrt{\frac{16-3\pi}{24} \cdot n},$

from which they also deviate at most by a constant. We prove that when n tends to infinity, the correlations Corr(Rec,Tra) and Corr(Rec,Vis)=Corr(Tra,Vis) converge to

$\frac{8-3\pi}{16-3\pi}\quad \mbox{and}\quad \sqrt{\frac{12-3\pi}{16-3\pi}}.$