Related papers: On the Hellmann-Feynman theorem for degenerate sta…
The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.
Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.
A rigorous quantum relativistic approach has been used to calculate the relationship between the decay laws of an unstable particle seen from two inertial frames moving with respect to each other. In agreement with experiment, it is found…
Using the Hellmann-Feynman theorem, a general comparison theorem is established for an eigenvalue equation of the form $(T+V)|\psi> = E|\psi>$, where $T$ is a kinetic part which depends only on momentums and $V$ is a potential which depends…
We prove that for a Wightman quantum field $\phi(x)$ the assumptions (i) positivity of the metric on the state space ${\cal H}$ of the theory (ii) the asymptotic condition in the form of Yang-Feldman equations and (iii) Klein-Gordon…
Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros…
We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),\alpha)$ so that the function $y$ and the order of fractional derivative $\alpha$ are varied in the minimization procedure. We derive…
We formulate part I of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. The main result is that all ground states can be constructed from the eigenvectors of a real, symmetric matrix with entries comprising…
Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the…
By using an exact analytical non-Hermitian formalism involving the full set of resonance (quasinormal) states and complex energy eigenvalues for quantum tunneling decay, we show that unitarity holds at any instant of time for the…
The quantum adiabatic theorem states that if a quantum system starts in an eigenstate of the Hamiltonian, and this Hamiltonian varies sufficiently slowly, the system stays in this eigenstate. We investigate experimentally the conditions…
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its…
In this work, we consider the thermal correction to the hyperfine interaction in hydrogen, deuterium, and the $^3$He$^+$ ion. This correction is effectively described by one-loop Feynman graphs in the framework of the quantum…
We study the accuracy of Kohn-Sham density functional theory (DFT) for warm- and hot-dense matter (WDM and HDM). Specifically, considering a wide range of systems, we perform accurate ab initio molecular dynamics simulations with…
The domain of convergence of a Heun function obtained through the Poincar\'{e}--Perron (P--P) theorem is not absolute convergence but conditional one [2]. We show that a uniqueness theorem is not available if we apply the P--P theorem into…
We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…
Using some resolution of singularities methods of the author, a generalization of a well-known theorem of Varchenko relating decay of oscillatory integrals to the Newton polyhedron is proven. They are derived from analogous results for…
We investigate the validity of quantum regression for a family of quantum Hamiltonians on a multipartite system leading to phase-damping reduced dynamics. After finding necessary and sufficient conditions for the CP-divisibility of the…
By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several…
We show (i) the existence of universal resource states for a certain class of linear Hamiltonians and (ii) the uselessness of highly entangled states for quantum metrology of linear Hamiltonians. We also show that random pure states are…