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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials
Calabi-Yau 曲线计数 4-folds
2023/4/23
I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4...
On the boundedness of effective potentials arising from string compactifications
the boundedness of effective potentials string compactifications Mathematical Physics
2012/6/30
We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative ans...
A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
Schrodinger equation Bloch decomposition time-splitting spectral method semiclassical asymptotics lattice potential
2012/5/24
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics ...
Parameter-free ansatz for inferring ground state wave functions of even potentials
Parameter-free ansatz state wave functions Quantum Physics Mathematical Physics
2011/10/9
Abstract: Schr\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM) are intimately linked, which entails the existence of a Legendre transform ...
Bound states of PT-symmetric separable potentials
PT-symmetric separable potentials High Energy Physics - Theory
2011/9/30
Abstract: All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form $V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$...
Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials
Random normal matrices Integral kernels Steepest descents method
2011/7/26
Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials.
On the new translational shape invariant potentials
new translational shape Gangopadhyaya Mallow Quantum Physics
2011/7/28
Abstract: Recently, several authors have found new translational shape invariant potentials not present in classic classifications like that of Infeld and Hull. For example, Quesne on the one hand and...
Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials
quantum mechanics supersymmetry orthogonal polynomials
2011/7/26
Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials.
Quantum mechanical potentials exactly solvable in terms of higher hypergeometric functions. I: The third-order case
Quantum mechanical higher hypergeometric third-order
2011/7/25
Abstract: We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of ...
Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
Fast Converging Path Integrals Time-Dependent Potentials II
2010/12/27
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for sim...
Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
Time-dependent potential Effective action Many-body system Imaginary time Real time
2010/11/25
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for sim...
Quantum Potentials with q-Gaussian Ground States
Quantum Potentials q-Gaussian Ground States
2010/11/23
We determine families of spherically symmetrical D-dimensional quantum potential functions
V (r) having ground state wavefunctions that exhibit, either in configuration or in momentum space,the form ...
Dissipative periodic waves, solitons and breathers of the nonlinear Schrodinger equation with complex potentials
periodic waves solitons the nonlinear Schrodinger equation
2010/11/18
Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a w...
We describe a way to construct supergravity models with an arbitrary inflaton potential V ( )
and show that all other scalar fields in this class of models can be stabilized at the inflationary traje...
Singular Short Range Potentials in the J-Matrix Approach
singular short-range potential J-matrix method
2010/11/4
We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differen...