Related papers: A note on Liouville theory
We outline a general method of obtaining exact solutions of Schroedinger equations with a position dependent effective mass. Exact solutions of several potentials including shape invariant potentials have also been obtained.
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/\mu)$ expansion, but in agreement with…
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…
The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We reformulate the heavy quark effective theory in the presence of a residual mass term, which has been taken to vanish in previous analyses. While such a convention is permitted, the inclusion of a residual mass allows us to resolve a…
We present an infinite set of higher equations of motion in N=2 supersymmetric Liouville field theory. They are in one to one correspondence with the degenerate representations and are enumerated in addition to the U(1) charge \omega by the…
In periodic, two-dimensional potentials a classical particle might be expected to escape from any finite region if it has enough energy to escape from a single cell. However, for a class of sinusoidal potentials in which the barriers…
We investigate exact enlarged controllability for time fractional diffusion systems of Riemann-Liouville type. The Hilbert uniqueness method is used to prove exact enlarged controllability for both cases of zone and pointwise actuators. A…
A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and…
The functional derivative of the effective action with respect to an external field is part of the equation of motion of this field if one-loop effects induced by quantum fluctuations or thermal fluctuations are included when minimizing the…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann-Liouville fractional derivatives, and that it is possible to…
We present a formalism to determine the imaginary part of a general chiral model in the derivative expansion. Our formalism is based on the worldline path integral for the covariant current that can be given in an explicit chiral and gauge…
Motivated by bubble nucleation in first order phase transitions, we question the validity of the effective potential for inhomogeneous configurations. In an attempt to get some insight into the importance of derivative terms, we analyze a…
The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary timescale, and the corresponding equilibrium free energy difference, is generalized to quantum systems. Using the…
Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…