Related papers: Exceptional points for associated Legendre functions of the second kind

Exceptional points for associated Legendre functions of the second kind

URL: http://arxiv.org/abs/2301.04092v1
Date: Sun, 8 Jan 2023 17:05:43 GMT
Title: Exceptional points for associated Legendre functions of the second kind
Authors: Tianye Liu, Daniel A. Norman and Philip D. Mannheim
Abstract summary: We consider the complex $nu$ plane structure of the associated Legendre function $Q-1/2-K_nu(coshrho)$. We find that for any noninteger value for $K$ $Q-1/2-K_nu(coshrho)$ has an infinite number of poles in the complex $nu$ plane.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We consider the complex $\nu$ plane structure of the associated Legendre function of the second kind $Q^{-1/2-K}_{\nu}(\cosh\rho)$. We find that for any noninteger value for $K$ $Q^{-1/2-K}_{\nu}(\cosh\rho)$ has an infinite number of poles in the complex $\nu$ plane, but for any negative integer $K$ there are no poles at all. For $K=0$ or any positive integer $K$ there is only a finite number of poles, with there only being one single pole (at $\nu=0$) when $K=0$. This pattern is characteristic of the exceptional points that appear in a wide variety of physical contexts. However, unusually for theories with exceptional points, $Q^{-1/2-K}_{\nu}(\cosh\rho)$ has an infinite number of them. Other than in the $PT$-symmetry Jordan-block case, exceptional points usually occur at complex values of parameters. While not being Jordan-block exceptional points themselves, the exceptional points associated with the $Q^{-1/2-K}_{\nu}(\cosh\rho)$ nonetheless occur at real values of $K$.

Related papers

The Communication Complexity of Approximating Matrix Rank [50.6867896228563]
We show that this problem has randomized communication complexity $Omega(frac1kcdot n2log|mathbbF|)$. As an application, we obtain an $Omega(frac1kcdot n2log|mathbbF|)$ space lower bound for any streaming algorithm with $k$ passes.
arXiv Detail & Related papers (2024-10-26T06:21:42Z)
Some new infinite families of non-$p$-rational real quadratic fields [0.0]
We give a simple methodology for constructing an infinite family of simultaneously non-$p_j$-rational real fields, unramified above any of the $p_j$. One feature of these techniques is that they may be used to yield fields $K=mathbbQ(sqrtD)$ for which a $p$-power cyclic component of the torsion group of the Galois groups of the maximal abelian pro-$p$-extension of $K$ unramified outside primes above $p$, is of size $pa
arXiv Detail & Related papers (2024-06-20T18:00:51Z)
Dimension Independent Disentanglers from Unentanglement and Applications [55.86191108738564]
We construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show that to capture NEXP, it suffices to have unentangled proofs of the form $| psi rangle = sqrta | sqrt1-a | psi_+ rangle where $| psi_+ rangle has non-negative amplitudes.
arXiv Detail & Related papers (2024-02-23T12:22:03Z)
Rationality of Four-Valued Families of Weil Sums of Binomials [6.752538702870792]
Weil sums of binomials of the form $WK,s_u=sum_x in K psi(xs - u x)$ are investigated. We show that if the Weil spectrum contains precisely four distinct values, then they must all be rational integers.
arXiv Detail & Related papers (2023-06-26T04:32:48Z)
A universal framework for entanglement detection under group symmetry [1.384055225262046]
We prove that all $(overlinepi_Aotimes pi_B)$-invariant quantum states are separable if and only if all extremal unital positive $(pi_A,pi_B)$-covariant maps are decomposable. $Phi(rho)=arho+brhoT+fracctextTr(rho)dtextId_d+ (1-a-b-c)textdiag(rho)
arXiv Detail & Related papers (2023-01-10T08:43:41Z)
Enlarging the notion of additivity of resource quantifiers [62.997667081978825]
Given a quantum state $varrho$ and a quantifier $cal E(varrho), it is a hard task to determine $cal E(varrhootimes N)$. We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.
arXiv Detail & Related papers (2022-07-31T00:23:10Z)
Quantum particle in a spherical well confined by a cone [0.0]
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone. The angular parts of the eigenstates depend on azimuthal angle $varphi$ and polar angle $theta$ as $P_lambdam(costheta)rm eimvarphi$.
arXiv Detail & Related papers (2022-07-04T15:32:41Z)
Simplest non-additive measures of quantum resources [77.34726150561087]
We study measures that can be described by $cal E(rhootimes N) =E(e;N) ne Ne$.
arXiv Detail & Related papers (2021-06-23T20:27:04Z)
Linear Bandits on Uniformly Convex Sets [88.3673525964507]
Linear bandit algorithms yield $tildemathcalO(nsqrtT)$ pseudo-regret bounds on compact convex action sets. Two types of structural assumptions lead to better pseudo-regret bounds.
arXiv Detail & Related papers (2021-03-10T07:33:03Z)
On the Complexity of Minimizing Convex Finite Sums Without Using the Indices of the Individual Functions [62.01594253618911]
We exploit the finite noise structure of finite sums to derive a matching $O(n2)$-upper bound under the global oracle model. Following a similar approach, we propose a novel adaptation of SVRG which is both emphcompatible with oracles, and achieves complexity bounds of $tildeO(n2+nsqrtL/mu)log (1/epsilon)$ and $O(nsqrtL/epsilon)$, for $mu>0$ and $mu=0$
arXiv Detail & Related papers (2020-02-09T03:39:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.