Related papers: A rapidity-independent parameter in the star-trian…
We quantify the stationary correlations between the optical mode and the relative mechanical mode of a ring cavity composed of a fixed mirror and two movable ones in a triangular design. The bipartite covariance matrix, is used to evaluate…
The number of minimal transitive star factorizations of a permutation was shown by Irving and Rattan to depend only on the conjugacy class of the permutation, a surprising result given that the pivot plays a very particular role in such…
We study oscillations and instabilities of relativistic stars using perturbation theory in general relativity and take into account the contribution of a dynamic spacetime. We present the oscillation spectrum as well as the critical values…
The radial velocity method for detecting extra-solar planets relies on measuring the star's wobble around the system's center of mass. Since this is an indirect method, we may ask if there are other dynamical effects that can mimic such…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
We revisit asteroseismology with quadrupolar wI modes and present universal relationships for its fundamental and first overtone. In contrast to relationships proposed in the literature, our universal relationships are capable of including…
Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate…
In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata…
An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is…
Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $\hbar$ is a time depending quantity,…
Neutron stars and quark stars are not only characterized by their mass and radius, but also by how fast they spin, through their moment of inertia, and how much they can be deformed, through their Love number and quadrupole moment. These…
Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…
We study the r-modes and rotational ``hybrid'' modes of relativistic stars. As in Newtonian gravity, the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey…
Many probability measures in the multiverse depend exponentially on some observable parameters, giving rise to potential problems such as youngness bias, Q-catastrophe etc. In this paper we explore a possibility that the exponential runaway…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
We study oscillations of slowly rotating relativistic barotropic as well as non-barotropic polytropic stars in the Cowling approximation, including first order rotational corrections. By taking into account the coupling between the polar…
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely…
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…
In this work, we consider simple systems that are influenced by Hamiltonians with time periodicity. Our analysis is mainly focussed on the density matrix approach and aims to solve the Liouville equation of motion from which one can extract…
We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal…