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We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on finite fragments of n-leg ladder rings and show jump-wise behavior of the ground state spin S{sub 0} as a function of fragment parameters.
Atkins' (1959) basic theory of third sound in thick films of superfluid He-4 is extended here to include a heat source for exciting third sound. A one-dimensional model obeying periodic boundary conditions is developed which can represent a variety of experimentally important configurations. General solutions for the model equations are found which give a complete description of third-sound waves in terms of displacement of the film surface, superfluid velocity, and temperature change as functions of space and time. Algebraic expressions for quantities that occur in general formulas are found for special excitation signals. The structure of third sound is calculated for the first time and the results are found to be inconsistent with previous findings. A direct method for accurately measuring the vaporization coefficient is also presented.
We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.
A monolayer of superfluid Fermi gas can be prepared within an optical dipole trap using the tight confinement along the chosen direction. In this case, Cooper pairs occupy the lowest state corresponding to the motion in the trapping potential. After switching off the trapping potential, the initially two-dimensional gas expands to the three-dimensional space. In the case of unitary s-wave interactions, the dynamics of Fermi gas expansion is treated in the framework of appropriately modified Gross–Pitaevskii equation. It is found that the superfluid gas expands significantly faster than the normal gas, in contrast to the situation characteristic of the initially three-dimensional gas. The available experimental data [P. Dyke et al., Phys. Rev. A 93, 011603 (2016)] are close to the predictions of the model under study.
Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U{sub c}=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott–Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model. -- Highlights: •The charge stiffness of the half-filled 1D Hubbard model is evaluated. •Its value is controlled by the model symmetry operator algebras. •We find that there is no charge ballistic transport at finite temperatures T>0. •The hidden U(1) symmetry controls the U=0 phase transition for T>0.
A simple rule of thumb based on resolution is not adequate to identify the best treatment of atomic displacements in macromolecular structural models. The choice to use isotropic B factors, anisotropic B factors, TLS models or some combination of the three should be validated through statistical analysis of the model refinement. In choosing and refining any crystallographic structural model, there is tension between the desire to extract the most detailed information possible and the necessity to describe no more than what is justified by the observed data. A more complex model is not necessarily a better model. Thus, it is important to validate the choice of parameters as well as validating their refined values. One recurring task is to choose the best model for describing the displacement of each atom about its mean position. At atomic resolution one has the option of devoting six model parameters (a ‘thermal ellipsoid’) to describe the displacement of each atom. At medium resolution one typically devotes at most one model parameter per atom to describe the same thing (a ‘B factor’). At very low resolution one cannot justify the use of even one parameter per atom. Furthermore, this aspect of the structure may be described better by an explicit model of bulk displacements, the most common of which is the translation/libration/screw (TLS) formalism, rather than by assigning some number of parameters to each atom individually. One can sidestep this choice between atomic displacement parameters and TLS descriptions by including both treatments in the same model, but this is not always statistically justifiable. The choice of which treatment is best for a particular structure refinement at a particular resolution can be guided by general considerations of the ratio of model parameters to the number of observations and by specific statistics such as the Hamilton R-factor ratio test.
We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a 'two negatives make a positive' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.
We study the physics of a three-component Fermi gas in an optical lattice, in the presence of a three-body constraint arising due to strong three-body loss. Using analytical and numerical techniques, we show that an atomic color superfluid phase is formed in this system and undergoes phase separation between unpaired fermions and superfluid pairs. This phase separation survives well above the critical temperature, giving a clear experimental signature of the three-body constraint.
We study superfluidity of supersolid phases of dipolar Bose gases in two-dimensional optical lattices. We perform linear stability analyses for the corresponding dipolar Bose-Hubbard model in the hard-core boson limit to show that a supersolid can have stable superflow until the flow velocity reaches a certain critical value. The critical velocity for the supersolid is found to be significantly smaller than that for a conventional superfluid phase. We propose that the critical velocity can be used as a signature to identify the superfluidity of the supersolid phase in experiment.
We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z 2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional Z 2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic X X interaction while keeping the local gauge symmetry intact. We find that the Z 2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.
We have investigated the magnetic properties and mapped out the phase diagram of the honeycomb magnet Na 2 Co 2 TeO 6 with Co 3d 7 in out-of-plane magnetic fields. This material has previously been proposed to show nearest-neighbor Kitaev interactions between Co spins and maybe even Kitaev quantum spin liquid behavior in high fields. At 0.01 T, we observe a thermal phase transition at T N = 27K, transitioning from a paramagnetic state to a canonical ferrimagnetic state. Upon increasing the magnetic field, a spin-floplike phase transition occurred before saturation of J = 1/2 between 10 K and T N . Below 10 K, a peak-dip-peak structure emerges between 10 and 17 T in the magnetic susceptibility (dM/dH) before the magnetic saturation, reminiscent of magnetization plateau behavior. The measurement of the magnetocaloric effect also shows dip-peak-dip behavior in this field range. Our data can be explained by an XXZ model with a single ion anisotropy and possibly small Kitaev and Γ exchange interactions. Finally, we also determined the magnetization saturation field that helps constrain the energy scale of the exchange interactions.
The original Drude model, proposed over a hundred years ago, is still used today for the analysis of optical properties of solids. Within this model, both the plasma frequency and quasiparticle scattering rate are constant, which makes the model rather inflexible. In order to circumvent this problem, the so-called extended Drude model was proposed, which allowed for the frequency dependence of both the quasiparticle scattering rate and the effective mass. In this work we will explore an alternative approach to the extended Drude model. Here, one also assumes that the quasiparticle scattering rate is frequency dependent; however, instead of the effective mass, the plasma frequency becomes frequency-dependent. This alternative model is applied to the high T{sub c} superconductor Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+δ} (Bi2212) with T{sub c} = 92 K, and the results are compared and contrasted with the ones obtained from the conventional extended Drude model. The results point to several advantages of this alternative approach to the extended Drude model.
Numerical analysis of the micromagnetic model was used to reveal the ‘resonance’ feature of relaxation processes in nanocrystalline thin magnetic films. This feature manifests itself in the form of sharp broadening of the ferromagnetic resonance (FMR) line at a certain frequency f{sub 1} depending on magnetic characteristics of the film, and is observed only in films the thickness of which exceeds some threshold value d{sub min}. Sharp broadening of the FMR line is accompanied by significant shift of the resonance field, whereas the shift value changes the sign at frequency ~ f{sub 1}. It was shown analytically that the nature of observed effects is associated with the two-magnon process of spin waves scattering on quasi-periodic magnetic microstructure – magnetization ‘ripple’. Obtained expressions for the threshold value of film thickness d{sub min} and frequency of maximum broadening of FMR line f{sub 1} agree well with the results of numerical computation of micromagnetic model.
In this paper, we developed a general mathematical model to estimate the nugget growth process based on the heat energy delivered into the welds by the resistance spot welding. According to the principles of thermodynamics and heat transfer, and the effect of electrode force during the welding process, the shape of the nugget can be estimated. Then, a mathematical model between heat energy absorbed and nugget diameter can be obtained theoretically. It is shown in this paper that the nugget diameter can be precisely described by piecewise fractal polynomial functions. Experiments were conducted with different welding operation conditions, such as welding currents, workpiece thickness, and widths, to validate the model and the theoretical analysis. All the experiments confirmed that the proposed model can predict the nugget diameters with high accuracy based on the input heat energy to the welds.
I recently introduced a closed-form description of propagated signaling phenomena in the membrane of an axon [R.F. Melendy, Journal of Applied Physics 118, 244701 (2015)]. Those results demonstrate how intracellular conductance, the thermodynamics of magnetization, and current modulation, function together in generating an action potential in a unified, closed-form description. At present, I report on a subsequent closed-form model that unifies intracellular conductance and the thermodynamics of magnetization, with the membrane electric field, E{sub m}. It’s anticipated this work will compel researchers in biophysics, physical biology, and the computational neurosciences, to probe deeper into the classical and quantum features of membrane magnetization and signaling, informed by the computational features of this subsequent model.
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Two models of classic XY antiferromagnets in three dimensions are studied by Monte Carlo simulation: the model on a simple cubic lattice with two extra intralayer exchanges and the model on a stackedtriangular lattice with an extra interlayer exchange. In suggested models, the order parameters are magnetization and two chiral parameters. A transition corresponds to breaking Double-Struck-Capital-Z {sub 2} Circled-Times Double-Struck-Capital-Z {sub 2} Circled-Times SO(2) symmetry. A distinct first order transition is found in both models.
We compare the recent temperature estimate for Geminga with neutron star cooling models. Because of its age (approximately 3.4 x 10(exp 5) yr), Geminga is in the photon cooling era. We show that its surface temperature (approximately 5.2 x 10(exp 5) K) can be understood by both types of neutrino cooling scenarios, i.e., slow neutrino cooling by the modified Urca process or fast neutrino cooling by the direct Urca process or by some exotic matter, and thus does not allow us to discriminate between these two competing schemes. However, for both types of scenarios, agreement with the observed temperature can only be obtained if baryon pairing is present in most, if not all, of the core of the star. Within the slow neutrino cooling scenario, early neutrino cooling is not sufficient to explain the observed low temperature, and extensive pairing in the core is necessary to reduce the specific heat and increase the cooling rate in the present photon cooling era. Within all the fast neutrino cooling scenarios, pairing is necessary throughout the whole core to control the enormous early neutrino emission which, without pairing suppression, would result in a surface temperature at the present time much lower than observed. We also comment on the recent temperature estimates for PSR 0656+14 and PSR 1055-52, which pertain to the same photon cooling era. If one assumes that all neutron stars undergo fast neutrino cooling, then these two objects also provide evidence for extensive baryon pairing in their core; but observational uncertainties also permit a more conservative interpretation, with slow neutrino emission and no pairing at all. We argue though that observational evidence for the slow neutrino cooling model (the 'standard' model) is in fact very dim and that the interpretation of the surface temperature of all neutron stars could be done with a reasonable theoretical a priori within the fast neutrino cooling scenarios only. In this case, Geminga, PSR 0656+14, and PSR 1055-52 all show evidence of baryon pairing down to their very centers.