Finite size effects and spontaneously broken symmetries: the case of theO(4) model

Finite volume numerical simulations of scalar models with continuous symmetry face strong finite size effects in the broken phase due to the presence of light Goldstone states. In the region where the light Goldstone bosons dominate the dynamics of the system universal finite size scaling formulae are predicted by chiral perturbation theory. Introducing a finite external source one can determine infinite volume, zero external source physical quantities from finite volume observables. Here we apply this theoretically controlled approach to the 4 dimensionalO(4) scalar model. All of our numerical results are in excellent agreement with the predicted finite size scaling forms. We confirm earlier results at zero external source where the infinite volume limit was approximated by projecting the fields to the direction of the magnetization.     

Symmetry Breaking in Finite Volume (Ⅱ)

Using a Hamiltonian approach and the adiabatic approximation, the low-lying spectrum of the lattice O (N) model in the broken phase is analyzed to the next to leading order. It is seen that these corrections appear as a systematic expansion in the inverse power of the lattice size L in the large volume limit.     

Ab initio theory of complex electronic ground state of superconductors: II.: Antiadiabatic state—Ground state of superconductors

Based on Q, P-dependent modification of the Born-Oppenheimer approximation (BOA), the ab initio theory of complex electronic ground state of superconductors is presented. As an illustrative example, application of the theory to superconductors of a different character and to the corresponding nonsuperconducting analogues is presented. It is shown that due to electron-phonon (EP) interactions, which drive system from adiabatic into antiadiabatic state, adiabatic translation symmetry is broken and system is stabilized in antiadiabatic state at distorted geometry with respect to adiabatic equilibrium high-symmetry structure. Stabilization effect in the antiadiabatic state is due to strong dependence of the electronic motion on the instantaneous nuclear kinetic energy, i.e. on the effect that is neglected on the adiabatic level within the BOA. At distorted geometry, antiadiabatic ground state is geometrically degenerated with fluxional nuclear configurations in the phonon modes that drive system into this state. It has been shown that until the system remains in antiadiabatic state, nonadiabatic polaron-renormalized phonon interactions are zero in the well-defined k-region of reciprocal lattice. This, along with geometric degeneracy of the antiadiabatic state, enables formation of mobile bipolarons that can move over lattice as supercarriers without dissipation. Moreover, it has been shown that due to EP interactions at transition into antiadiabatic state, k-dependent gap in one-electron spectrum has been opened. Gap opening is associated with shift of the original adiabatic Hartree-Fock orbital energies and with the k-dependent change in density of states of particular band(s) at Fermi level. Corrected one-particle spectrum enables to derive thermodynamic properties in full agreement with corresponding thermodynamic properties of superconductors.Based on the complex ab initio theory, it has been shown that Fröhlich's effective attractive electron-electron interaction term represents correction to electron correlation energy at transition from adiabatic into antiadiabatic state due to EP interactions. It has been shown that increased electron correlation is a consequence of stabilization of the system in superconducting electronic ground state, but not the reason for its formation.     

Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice

Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which develop Néel and three-sublattice stripelike long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irreducible representation, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.     

随机共振问题Fokker-Planck方程的数值研究

本文用有限差分方法对一随机共振的Fokker-Planck方程的主要性质进行了广泛的数值研究。结果表明,当绝热近似条件ω?D△V和小信号近似条件A?1得到满足时,以往的解析近似理论结果与数值结果符合;当驱动强度增加时,则系统表现出明显的决定性非线性振动行为。然而,就随机共振问题本身而言,绝热近似解析理论概括了在双稳系统中发生的随机共振的主要性质。 关键词：     

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.     

Superconductivity with broken time-reversal symmetry

This presentation gives an overview over phenomena occurring in unconventional superconductors with broken time-reversal symmetry. The best-known effect related with broken time-reversal symmetry is intrinsic magnetism observable by μSR. In many cases this magnetism is connected to the appearance of chiral quasiparticle edge states which originate from topological properties of the superconducting order parameter. Time-reversal symmetry can also be broken only locally and has then strong influence of the local quasiparticle spectrum. The existence of vortices with fractional flux pinned strongly on domain walls in time-reversal symmetry breaking superconductors leads to unusual flux flow behavior.     

Magneto-optics of three-dimensional quantum dots: a real time, time-dependent local spin–density approach

We perform adiabatic time-dependent local spin–density approximation (TDLSDA) calculations in real time of the excitation spectrum of three-dimensional quantum dots (QD's) in magnetic fields of arbitrary direction. In the case of parabolic confinement and electric dipole modes, the calculations reproduce exactly the generalized Kohn theorem, which is a stringent test of the numerical accuracy achieved by our practical implementation of TDLSDA. We apply the method to the study of spin dipole modes in a QD. Real time TDLSDA can be more efficient than Green's function methods to compute the dynamical properties of confined electrons, especially when the finite thickness of the system has to be taken into account. As an illustration, we obtain the dipole spin modes and the acoustic modes of vertical diatomic artificial quantum molecules at zero magnetic field.     

Microcanonical mean-field thermodynamics of self-gravitating and rotating systems

We derive the global phase diagram of a self-gravitating N-body system enclosed in a finite three-dimensional spherical volume V as a function of total energy and angular momentum, employing a microcanonical mean-field approach. At low angular momenta (i.e., for slowly rotating systems) the known collapse from a gas cloud to a single dense cluster is recovered. At high angular momenta, instead, rotational symmetry can be spontaneously broken and rotationally asymmetric structures (double clusters) appear.     

Effective Hamiltonian of the Jaynes–Cummings model beyond rotating-wave approximation

The Jaynes–Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes–Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the highfrequency regime. In contrast to the Z_2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1)symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.     

General Adiabatic Evolution with a Gap Condition

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. The presence of eigenilpotents in the spectral decomposition of the generator typically leads to solutions which grow exponentially fast in some inverse power of the adiabaticity parameter, even for real spectrum. In turn, this forbids the evolution to follow all instantaneous eigenprojectors of the generator in the adiabatic limit. Making use of superadiabatic renormalization, we construct a different set of time-dependent projectors, close to the instantaneous eigenprojectors of the generator in the adiabatic limit, and an approximation of the evolution semigroup which intertwines exactly between the values of these projectors at the initial and final times. Hence, the evolution semigroup follows the constructed set of projectors in the adiabatic regime, modulo error terms we control.     

Spin Interactions in bcc and fcc Fe beyond the Heisenberg Model

Usually, the adiabatic magnetic exchange-energy hypersurface is parametrized in terms of the bilinear Heisenberg interactions in pairs of atoms. For general magnetic configurations, this model is not complete even if it includes pairs with up to infinite interatomic distances. In contrast, the modeling by an in principle infinite spin-cluster expansion is complete for all conceivable magnetic configurations. In the present Letter, it is shown for bcc and fcc iron that a very accurate representation can be reached with a finite expansion with 20 terms which include biquadratic or multispin non-Heisenberg interactions.     

Replica Method and Finite Volume Corrections

In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of additional corrections: these corrections can be interpreted as arising from fluctuations in the size of the blocks in the replica approach. The computation suggests a new approach for deriving the replica broken results in a rigorous way.     

Three-Body Physics in a Finite Volume

Three particles with large two-body scattering lengths display universal properties including a spectrum of three-body bound states called “Efimov trimers”. I calculate the spectrum of three identical bosons inside a finite cubic box below the three-body breakup threshold. The dependence of the spectrum on the box size and the effects of the breakdown of spherical symmetry are investigated using effective field theory. The renormalization of the effective field theory in the finite volume is explicitly verified. The study of the three-nucleon system inside a finite cubic volume provides a tool for the understanding of Lattice QCD results. I study the triton in a finite volume at physical and unphysical pion masses.     

A non-perturbative analysis in finite volume gauge theory

We discuss SU(2) gauge theory on a three-torus using a finite volume expansion. Our discovery of natural coordinates allows us to obtain continuum results in a region where Monte Carlo data are also available. The obtained results agree well with the perturbative and semiclassical analysis for small volumes, and there is fair agreement with the Monte Carlo results in intermediate volumes. The simple picture which emerges for the approximate low energy dynamics is that of three interacting particles enclosed in a sphere, with zero total “angular momentum”. The validity of an adiabatic approximation is investigated. The fundamentally new understanding gained, is that non-perturbative dynamics can be incorporated by imposing boundary conditions which arise through the nontrivial topology of configuration space.     

General semi-classical method for collective motion and its connection with the Rowe-Basserman and marumori theories,and adiabatic limits

In recent work, we have shown that in the adiabatic limit (large amplitude, small momentum), time-dependent Hartree-Fock theory (TDHF) yields a well-defined theory of large-amplitude collective motion which provides an essentially unique construction for a collective hamiltonian. An alternative theory, put forward by Rowe and Basserman and by Marumori is, apparently, not restricted to small momenta. We describe a general framework for the study of collective motion in the semi-classical limit without limitation on the size of coordinates or momenta, which includes all previous methods as limiting cases. We find it convenient, as in the past, to consider two general systems: first, a system with n degrees of freedom and no special permutation symmetry, and, second, a system of fermions described in TDHF. For both systems the problem can be formulated as a search for a hamiltonian flow confined to a finite-dimensional hypersurface in a phase space, which itself may be finite- or infinite-dimensional. Though, in general, there are no exact solutions to this problem, we can formulate consistent approximation schemes corresponding to both the adiabatic and Rowe-Basserman, and Marumori limits. We also show how to extend the momentum expansion, which underlies the adiabatic approximation, to higher orders in the momentum. We thereby confirm the structure of the theory found in our previous work.     

An evolution of adiabatic matter: a case for the quasistatic regime

We establish the connection between the standard ADM 3+1 treatment of matter with its characteristic equivalent, in the context of spherical symmetry. The flux-conservative rendition of the fluid equations are obtained. Considering adiabatic distributions of perfect fluid, we evolve the system using the so-called post-quasi-static approximation in radiation coordinates. We obtain an adiabatic matter evolution in the quasi-static regime or slow motion, which is not shear-free nor geodesic.     

Inflaton field potential producing an exactly flat spectrum of adiabatic perturbations

Presented in this letter is the exact solution of the problem of finding the potential of an inflaton scalar field for which adiabatic perturbations generated during a de Sitter (inflationary) stage in the early Universe have an exactly flat (or, the Harrison-Zeldovich) initial spectrum. This solution lies outside the scope of the slow-roll approximation and higher-order corrections to it. The potential found depends on two arbitrary physical constants, one of which determines the amplitude of the perturbations. For small (zero) values of the other constant, a long (infinite) inflationary stage with slow rolling of the inflaton field exists.