Two-Loop Effective Potential of λø24 Without Cut-Off Dependence

The effective potential of λø⁴ theory in two-dimensional spacetime is calculated up to twoloop level in an operator approach (or causd approach) without divergence. It reveals a second-order phase transition. A further discussion about the rdation between the convexity of the full effective potential and phase transition is given. We propose a modified Feynman path integral (FPI) representation of λø₂⁴ and sketch a plausible proof for the convexity of its full effective potential.     

Strict Convexity of the Free Energy for a Class of Non-Convex Gradient Models

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. We show using a one-step multiple scale analysis the strict convexity of the surface tension at high temperature. This is an extension of Funaki and Spohn’s result [8], where the strict convexity of potential was crucial in their proof. Supported by the DFG-Forschergruppe 718 ‘Analysis and stochastics in complex physical systems’.     

Quantum electrodynamics in 2 + 1 dimensions, confinement, and the stability of U(1) spin liquids

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.     

Energy of N Cooper pairs by analytically solving the Richardson-Gaudin equations for conventional superconductors

This Letter provides the solution to a yet unsolved basic problem of solid state physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50?yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the N-pair energy depends on N as N(N-1) only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.     

QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

Inequalities for light nuclei in the Wigner symmetry limit

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three- and four-nucleon force terms.     

Quantum extremism: effective potential and extremal paths

The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time. It has been shown that canonical and path-integral approaches may yield different results, thus resolving the convexity problem. We discuss the transferal of these treatments to Minkowskian space-time, which also necessitates a careful discussion of precisely which field configurations give the dominant contributions to the path integral. In particular, we study the effective potential for the N=1 linear sigma model.     

Superfluid-insulator transitions of the fermi gas with near-unitary interactions in a periodic potential

We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period a_{L}, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V=V_{c}. We compute the universal ratio V_{c}ma_{L};{2}/variant Planck's over 2pi;{2} at N=infinity in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.     

Orbifold equivalence and the sign problem at finite baryon density

We point out that SO(2N(c)) gauge theory with N(f) fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential μ(B). One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N(c)) theory is particularly interesting because a wide class of observables in the SO(2N(c)) theory coincide with observables in QCD in the large N(c) limit, as we show using the technique of large N(c) orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite μ(B) provided one adds appropriate deformation terms to the SO(2N(c)) theory. This opens up the prospect of learning about QCD at finite μ(B) using lattice studies of the SO(2N(c)) theory.     

Chiral susceptibility and chiral phase transition in Nambu–Jona-Lasinio model

We give a general relation between the chiral susceptibility and the thermodynamical potential and a relation between the chiral susceptibility and the condition for furcations to appear in the Wigner solution(s) in the Nambu–Jona-Lasinio (NJL) model. We find that the chiral susceptibility is a quantity able to represent the appearance of furcation in the solution(s) of the gap equation and the concavo–convexity of the thermodynamical potential in the NJL model. It indicates that the chiral susceptibility can identify the stability of the states and the chiral phase transition in NJL model. We propose that analyzing the chiral susceptibility may play an important role in studying the chiral phase transition in approaches superior to the NJL model.     

Bifurcation structures and dominant modes near relative equilibria in the one-dimensional discrete nonlinear Schrödinger equation

We investigate the bifurcation structure of a family of relative equilibria of a ring of seven oscillators described by the discrete nonlinear Schrödinger equation (DNLSE) when the period of these orbits and a suitable defect act as bifurcation parameters. We find a reduced Hamiltonian that gives substantial insight into the dynamics of this system. The convexity of this Hamiltonian at given nonresonant equilibria supports the stability of nearby quasiperiodic solutions. We show that the local loss of convexity in the reduced Hamiltonian is determined by the Hessian of its integrable part in the family of relative equilibria under study. Stable quasiperiodic solutions are studied by considering the power spectral densities of a set of suitable fast and slow actions, whose origin is suggested by the averaging principle. We also show that the return times form an optimal embedding to characterize the system dynamics. We show that the power spectral density of a suitable interference signal, arising from a ring of Bose-Einstein condensates and described by the DNLSE, has a single prominent peak at the breather-like relative equilibria.     

Negative Goos-Hänchen shift on a concave dielectric interface

We study the Goos-H?nchen shift (GHS) on a curved surface through numerical simulation by the boundary element method. A negative GHS is first discovered on a concave dielectric interface below the critical angle, accompanied by a large positive GHS on the convexity. The simulation shows that the GHS on a planar interface is the composition of the GHS from a concave and the corresponding convex interface. This work will enrich the study of the GHS for different curved surfaces, which will have potential applications in micro-optics and near-field optics.     

Exact relaxation dynamics of a localized many-body state in the 1D Bose gas

Through an exact method, we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreases, which suggests the existence of off-diagonal long-range order. We show a recurrence phenomenon for a small number of particles such as N=20.     

On Possible S-Wave Bound States for an N\bar{N} System Within a Constituent Quark Model

We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the N\bar{N} in S-wave (the quarks in the nucleons N and \bar{N}, and the two nucleons relatively as well, are in S wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of p\bar{p} in J/ψ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight S-wave bound state of six quarks, then the quantum number of the bound state is very likely to be I=1, J^PC=0^-+.     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Investigation of one class of Bargman-type potentials

For the spectral problem on the half-axis we derive an expression for the potential with N levels of discrete spectrum that are positioned in a previously determined fashion. We obtain wave functions for the discrete spectrum, Yost’s solution, and the continuous-spectrum functions. We show that the Yost function for this potential is a rational fractional function of the wave number k and, consequently, the potential itself is a potential of Bargman type. Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34–39, May, 1998.     

中能重离子碰撞中的中子(质子)发射的同位旋效应

利用同位旋相关的量子分子动力学,对中能重离子碰撞过程中的中子和质子发射的同位旋效应进行了分析.计算结果表明在有动量相关作用条件下,在很宽的能量和碰撞参数范围内,缺中子碰撞系统的中子(质子)发射数强烈地依赖于同位旋相关的核子–核子碰撞截面,而较弱地依赖于对称势.在对丰中子碰撞系统的研究中,上述规律减弱.这样就可以通过实验上对缺中子碰撞系统的中子(质子)发射数的探测,来提取介质中同位旋相关核子–核子碰撞截面的知识.     

Landau levels and Riemann zeros

The number N(E) of complex zeros of the Riemann zeta function with positive imaginary part less than E is the sum of a "smooth" function N[over ](E) and a "fluctuation." Berry and Keating have shown that the asymptotic expansion of N[over ](E) counts states of positive energy less than E in a "regularized" semiclassical model with classical Hamiltonian H=xp. For a different regularization, Connes has shown that it counts states "missing" from a continuum. Here we show how the "absorption spectrum" model of Connes emerges as the lowest Landau level limit of a specific quantum-mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of N(E).     

Horizon ratio bound for inflationary fluctuations

We demonstrate that the gravity wave background amplitude implies a robust upper bound on the wavelength-to-horizon ratio at the end of inflation: lambda/H(-1) less than or approximately equal e(60), as long as the cosmic energy density does not drop faster than radiation subsequent to inflation. This limit implies that N, the number of e-folds between horizon exit and the end of inflation for wave modes of interest, is less, similar 60 plus a model-dependent factor-for vast classes of slow-roll models, N less than or approximately equal 67. As an example, this bound solidifies the tension between observations of the cosmic microwave background anisotropies and chaotic inflation with a phi(4) potential by closing the escape hatch of large N (<62).     

Scaling and decay in periodically driven scattering systems

We investigate irregular scattering in a periodically driven Hamiltonian system of one degree of freedom. The potential is asymptotically attracting, so there exist parabolically escaping scattering orbits, i.e. orbits with asymptotic energy E(out)=0. The scattering functions (i.e. the asymptotic out-variables as functions of an asymptotic in-variable) show a characteristic algebraic scaling in the vicinity of these orbits. This behavior is explained by asymptotic properties of the interaction. As a consequence, the number N(Deltat) of temporarily bound particles decays algebraically with the delay time Deltat, although no KAM scenario can be found in phase space. On the other hand, we find the number N(n) of temporarily bound particles to decay exponentially with the number n of zeros of x(t).