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Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented…

Statistical Mechanics · Physics 2010-12-23 Victor P. Berezovoj , Glib I. Ivashkevych , Mikhail I. Konchatnij

We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard type one dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time independent classical Hamiltonian is of non-standard…

Quantum Physics · Physics 2012-09-07 V. Chithiika Ruby , M. Senthilvelan , M. Lakshmanan

We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold $M$ as part of the construction of quantum geodesics on the algebra $D(M)$ of differential operators. Geodesic motion arises here as an…

General Relativity and Quantum Cosmology · Physics 2025-11-10 Edwin Beggs , Shahn Majid

We calculate the eigenvalues and their corresponding eigenfunctions of the Bohrs collective Hamiltonian with the help of the modified Poschl-Teller potential model within -unstable structure. Our numerical results for the ground state beta…

Nuclear Theory · Physics 2017-12-06 Nahid Soheibi , Majid Hamzavi , Mahdi Eshghi , Sameer M. Ikhdair

The spectrum of a one-dimensional Hamiltonian with potential $V(x)=ix^2$ for negative $x$ and $V(x)=-ix^2$ for positive $x$ is analyzed. The Schr\"odinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of…

Quantum Physics · Physics 2014-01-24 E. M. Ferreira , J. Sesma

We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like…

Optics · Physics 2018-11-14 Yaniv Eliezer , Alon Bahabad , Boris A. Malomed

We consider the canonical quantisation of spherically symmetric spacetimes within unimodular gravity, leaving sign choices in the metric general enough to include both the interior and exterior Schwarzschild-(Anti-)de Sitter spacetime. In…

High Energy Physics - Theory · Physics 2025-06-12 Steffen Gielen , Sofie Ried

In this work, we apply the generalised Feshbach Villars transformation (GFVT) to spin-0 scalar fields in a Schwarzschild gravitational background. Starting from the covariant Klein Gordon equation, we reformulate the dynamics in the FV…

General Relativity and Quantum Cosmology · Physics 2025-09-17 Sarra Garah , Abdelmalek Boumali

We prove that there exist K\"{a}hler manifolds that are not homotopy equivalent to a quotient of complex hyperbolic space but which admit a Riemannian metric with nonpositive curvature operator. This shows that K\"{a}hler manifolds do not…

Differential Geometry · Mathematics 2024-01-31 Barry Minemyer

We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schr\"odinger operators on compact Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral…

Spectral Theory · Mathematics 2021-03-17 Jean Lagacé , Simon St-Amant

The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…

Mathematical Finance · Quantitative Finance 2023-07-04 Tongseok Lim

In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…

General Relativity and Quantum Cosmology · Physics 2025-11-03 Etera R. Livine , Yuki Yokokura

For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…

Computational Finance · Quantitative Finance 2014-06-26 Antoine Jacquier , Matthew Lorig

We consider relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry. We utilise Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in…

General Relativity and Quantum Cosmology · Physics 2022-01-10 Qasem Exirifard , Ebrahim Karimi

We explore quasinormal modes (QNMs) of the Schwarzschild black hole under a noncommutative (NC) deformation of spacetime, constructed via a Drinfeld twist formalism. In this approach, the usual Regge--Wheeler (axial) and Zerilli (polar)…

General Relativity and Quantum Cosmology · Physics 2025-03-20 Nikola Herceg , Tajron Jurić , A. Naveena Kumara , Andjelo Samsarov , Ivica Smolić

We identify and study a class of hyperbolic 3-manifolds (which we call Macfarlane manifolds) whose quaternion algebras admit a geometric interpretation analogous to Hamilton's classical model for Euclidean rotations. We characterize these…

Geometric Topology · Mathematics 2019-06-28 Joseph A. Quinn

We renormalize the Chern-Simons invariant for convex-cocompact hyperbolic 3-manifolds by finding the asymptotics along an equidistance foliation. We prove that the metric Chern-Simons invariant has an exponentially divergent term given by…

Differential Geometry · Mathematics 2025-06-25 Dongha Lee

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge $Q$ off a Schwarzschild black hole, showing a remarkably…

We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…

Pricing of Securities · Quantitative Finance 2010-11-23 Giacomo Bormetti , Valentina Cazzola , Danilo Delpini

The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…

Quantum Physics · Physics 2009-11-06 S. A. Fulling