arXiv subjects

Yan He

Publications and source records attributed to Yan He.

At least 91 records · Page 5Linked to original sources

arXiv2019

Interaction phenomena between lump and solitary wave of a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles

In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained. Their interaction phenomena is shown in some 3d graphs and contour plots, which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution,interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented.

nlin.PS↗

arXiv2019

Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes

The dynamics of two-dimensional (2D) topological quadrupole insulator (TQI) and Chern insulator (CI) after the real-space configuration is transformed from a cylinder or Mobius strip to open boundary condition (OBC) and vice versa is analyzed. Similar dynamics of both models are observed, but the quadrupole corner states of the TQI makes the signatures more prominent. After the systems transform from a cylinder or Mobius strip to OBC, the occupation of the corner state of the TQI and the edge state of the CI exhibits steady-state behavior. The steady-state values depend on the ramping rate of the configuration transformation, manifesting a type of quantum memory effect. On the other hand, oscillatory density ripples from the merging of edge states persist after the systems transform from OBC to a cylinder or Mobius strip. If the final configuration is a cylinder, the density ripples are along the edges of the cylinder. In contrast, the density ripples can traverse the bulk after the systems transform from OBC to a Mobius strip. The transformation of real-space topology thus can be inferred from the dynamical signatures of the topological edge states.

cond-mat.mes-hall↗

arXiv2019

A generalized subspace theorem for closed subschemes in subgeneral position

In this paper, we extend the recent theorem of G. Heier and A. Levin [arXiv:1712.02456] on the generalization of Schmidt's subspace theorem and Cartan's Second Main Theorem in Nevanlinna theory to closed subschemes located in $l$-subgeneral position, using the generic linear combination technique due to Quang.

math.NT↗

arXiv2019

A class of fully nonlinear equations arising in conformal geometry

In this paper, we consider a class of fully nonlinear equations on closed smooth Riemannian manifolds, which can be viewed as an extension of $σ_k$ Yamabe equation. Moreover, we prove local gradient and second derivative estimates for solutions to these equations and establish an existence result associated to them.

math.DG↗

arXiv2019

Nonlocal behaviors of spin correlations in the Haldane-Shastry model

The nonlocal factors of spin correlations are introduced for lattice spin models. Based on this concept, we investigate the nonlocal behavior of the Haldane-Shastry model with or without ring frustration. The ground state and spin correlations of the Haldane-Shastry model are calculated for both even and odd number of spins, then the nonlocal factors can be deduced analytically. It is found that the nonlocal factor due the ring frustration is the same as the Heisenberg model.

cond-mat.stat-mech↗

arXiv2019

A Pogorelov estimate and a Liouville type theorem to parabolic $k$-Hessian equations

We consider Pogorelov type estimates and Liouville type theorems to parabolic $k$-Hessian equations of the form $-u_t σ_k (D^2u) =1$ in $\mathbb{R}^n\times (-\infty, 0]$. We derive that any \textbf{$k+1$-convex-monotone} solution to $-u_t σ_k (D^2u) =1$ when $u(x,0)$ satisfies a quadratic growth and $0<m_1\le -u_t\le m_2$ must be a linear function of $t$ plus a quadratic polynomial of $x$.

math.AP↗

arXiv2019

A Liouville type theorem to $2$-Hessian equations

In this paper, we proved that any 2-convex solution $u$ of $σ_2(D^2u)=1$ with a quadratic growth must be a quadratic polynomial in $\mathbb{R}^n\ (n\geq 3 )$ by using a Pogorelov estimate and the global gradient estimate. And we give a positive answer to the unresolved issue in \cite{CX}.

math.AP↗

arXiv2019

A Rigidity theorem for parabolic 2-Hessian equations

In this paper, we consider the entire solutions to the parabolic $2$-Hessian equations of the form $-u_tσ_2(D^2 u)=1$ in $\mathbb{R}^n\times (-\infty,0]$. We prove some rigidity theorems for the parabolic $2$-Hessian equations in $\mathbb{R}^n\times (-\infty,0]$ by establishing Pogorelov type estimates for $2$-convex-monotone solutions of the parabolic $2$-Hessian equations.

math.AP↗

arXiv2019

Three dimensional two-band Floquet topological insulator with $Z_2$ index

We present a class of three dimensional (3D) two-band Floquet topological insulators constructed from two-dimensional Floquet topological insulators with a $Z$ topological index. It is shown that the 3D two-band Floquet topological insulator has a $Z_2$ topological index, whose value can be obtained by numerical calculations or by using a relation to the winding number. The classification of the 3D $Z_2$ Floquet topological insulator, however, cannot be attributed to the stable homotopy groups. Thus, it is an example outside the proposed K-theory classifications of Floquet topological insulators. We also analyze the edge modes of the 3D $Z_2$ Floquet topological insulator and find the parity of the number of edge modes reflects the bulk $Z_2$ index.

cond-mat.mes-hall↗

arXiv2018

Ring frustration and factorizable correlation functions of critical spin rings

Basing on the exactly solvable prototypical model, the critical transverse Ising ring with or without ring frustration, we establish the concept of nonlocality in a many-body system in the thermodynamic limit by defining the nonlocal factors embedded in its factorizable correlation functions. In the context of nonlocality, the valuable traditional finite-size scaling analysis is reappraised. The factorizable correlation functions of the isotropic $XY$ and the spin-1/2 Heisenberg models are also demonstrated with the emphasis on the effect of ring frustration.

cond-mat.stat-mech↗

arXiv2018

Thermal Uhlmann Chern number from the Uhlmann connection for extracting topological properties of mixed states

The Berry phase is a geometric phase of a pure state when the system is adiabatically transported along a loop in its parameter space. The concept of geometric phase has been generalized to mixed states by the so called Uhlmann phase. However, the Uhlmann phase is constructed from the Uhlmann connection that possesses a well defined global section. This property implies that the Uhlmann connection is topologically trivial and as a consequence, the corresponding Chern character vanishes. We propose modified Chern character whose integral gives the thermal Uhlmann Chern number, which is related to the winding number of the mapping defined by the Hamiltonian. Therefore, the thermal Uhlmann Chern number reflects the topological properties of the underlying Hamiltonian of a mixed state. By including the temperature dependence in the volume integral, we also introduce the non-topological thermal Uhlmann Chern number which varies with temperature but is not quantized at finite temperatures. We illustrate the applications to a two-band model and a degenerate four-band model.

cond-mat.mes-hall↗

arXiv2018

BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.

cond-mat.supr-con↗

arXiv2018

$q$-deformed Fermion in Many-Particle Systems and Its Application to BCS Theory

In recent decades, there have been increasing interests in quantum statistics beyond the standard Fermi-Dirac and Bose-Einstein statistics, such as the fractional statistics, quon statistics, anyon statistics and quantum groups, since they can provide some new insights into the cosmology, nuclear physics and condensed matter. In this paper, we study the many-particle system formed by the $q$-deformed fermions ($q$-fermion), which is realized by deforming the quantum algebra of the anticommutation relations. We investigate from a standard perspective of the finite temperature field theory and try to construct the finite temperature Green's function formalism for the free many-$q$-fermion system, then generalize it to the well known interacting fermionic system, the superconductor, and finally obtain a consistent $q$-deformed BCS ($q$BCS) theory. At low temperature, this theory predicts a Sarma-like ordered phase, and we call it the $q$-deformed Sarma phase. It also presents a symmetric phase diagram in the parameter space and new thermodynamic relations.

cond-mat.stat-mech↗

arXiv2017

Topology, edge states, and zero-energy states of ultracold atoms in 1D optical superlattices with alternating onsite potentials or hopping coefficients

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold-atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.

cond-mat.quant-gas↗

arXiv2017

Dynamic density structure factor of a unitary Fermi gas at finite temperature

We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near a Feshbach resonance at finite temperature. The study is based on a gauge invariant linear response theory. The theory is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects some important restrictions like the $f$-sum rule. Our numerical results show that the dynamic density structure factor at large incoming momentum and at half recoil frequency has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. This qualitatively agrees with the recent Bragg spectroscopy experiment results. We also present the results at small incoming momentum.

cond-mat.quant-gas↗

arXiv2017

The boundary effects of transverse field Ising model

Advance in quantum simulations using trapped ions or superconducting elements allows detailed analysis of the transverse field Ising model (TFIM), which can exhibit a quantum phase transition and has been a paradigm in exactly solvable quantum systems. The Jordan-Wigner transformation maps the one-dimensional TFIM to a fermion model, but additional complications arise in finite systems and introduce a fermion-number parity constraint when periodic boundary condition (PBC) is imposed. By constructing the free energy and spin correlations with the fermion-number parity constraint and comparing the results to the TFIM with open boundary condition, we show that the boundary effects can become significant for the anti-ferromagnetic TFIM with odd number of sites at low temperature.

cond-mat.stat-mech↗

arXiv2017

Shear Viscosity of Uniform Fermi Gases with Population Imbalance

The shear viscosity plays an important role in studies of transport phenomena in ultracold Fermi gases and serves as a diagnostic of various microscopic theories. Due to the complicated phase structures of population-imbalanced Fermi gases, past works mainly focus on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi gases with tunable attractive interactions at finite temperatures by using a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. In the unitary and BEC regimes, the shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. In the weak BEC regime the excess fermions also suppress the noncondensed pairs at low polarization, and we found a minimum in the ratio of shear viscosity and relaxation time. To help constrain the relaxation time from linear response theory, we derive an exact relation connecting some thermodynamic quantities and transport coefficients at the mean-field level for unitary Fermi superfluids with population imbalance. An approximate relation beyond mean-field theory is proposed and only exhibits mild deviations from numerical results.

cond-mat.quant-gas↗

arXiv2017

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

The shear viscosity has been shown to be equal to the product of pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. By using the mean-field BCS-Leggett theory with a gauge-invariant linear response theory for unitary Fermi superfluids, we present an explicit relation between thermodynamic quantities, including the pressure and chemical potential, and transport coefficients, including the shear viscosity, superfluid density, and anomalous shear viscosity from momentum transfer via Cooper pairs. The relation is modified when pairing fluctuations associated with noncondensed Cooper pairs are considered. Within a pairing fluctuation theory consistent with the BCS-Leggett ground state, we found an approximate relation for unitary Fermi superfluids. The exact mean-field relation and the approximate one with pairing flucutaions advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which can be otherwise difficult to measure.

cond-mat.quant-gas↗