Related papers: On the second minimax level for the scalar field e…
Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties…
We study the large $N$ limit of $O(N)$ scalar field theory with classically marginal $\phi^6$ interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large $N$. We find…
The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the…
The Hadamard state condition is used to analyze the local constraints on the two-point function of a quantum field conformally coupled to a background geometry. Using these constraints we develop a scalar tensor theory which controls the…
We study a minimally coupled charged scalar field in a charged Lifshitz background. For z=2, we find an analytic expression for the corresponding low energy retarded Green's function. Unlike the RN-AdS case, the position of the superfluid…
We show that, as a result of non-linear self-interactions, it is feasible, at least in light of the bounds coming from terrestrial tests of gravity, measurements of the Casimir force and those constraints imposed by the physics of compact…
The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…
We study nonlinear ground states of the Gross-Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas-Fermi approximation of ground states on various spatial scales was…
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most…
We present the exact and explicit solution of the principal chiral field in two dimensions for an infinitely large rank group manifold. The energy of the ground state is explicitly found for the external Noether's fields of an arbitrary…
This paper is devoted to the study of the two-dimensional Dirac-Coulomb operator in presence of an Aharonov-Bohm external magnetic potential. We characterize the highest intensity of the magnetic field for which a two-dimensional magnetic…
As a quantum gravity cut-off, the species scale $\Lambda_s$ gets naturally compared to the energy scale of a scalar potential $V$ in an EFT. In this note, we compare the species scale, its rate $|\nabla \Lambda_s|/\Lambda_s$ and their field…
We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the…
A new idea to approximate the second eigenfunction and the second eigenvalue of $p$-Laplace operator is given. In the case of the Dirichlet boundary condition, the scheme has the restriction that the positive and the negative part of the…
We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.
We consider nonlinear second order elliptic problems of the type \[ -\Delta u=f(u) \text{ in } \Omega, \qquad u=0 \text{ on } \partial \Omega, \] where $\Omega$ is an open $C^{1,1}$-domain in $\mathbb{R}^N$, $N\geq 2$, under some general…