Related papers: The Riemann Hypothesis Emerges in Dynamical Quantu…
A simple ordinary differential equation is derived governing the red-shifts of wave-fronts propagating through a non-stationary spherically symmetric space-time. Approach to an event horizon corresponds to approach to a fixed point; in…
We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagentic interactions in the presence of a longitudinal field which renders the model non-integrable. The dynamics of the spin chain is…
We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the $S$-wave Jost function at zero energy and in identifying it with the Riemann $\xi(s)$…
An incomplete Riemann zeta function can be expressed as a lower-bounded, improper Riemann-Liouville fractional integral, which, when evaluated at $0$, is equivalent to the complete Riemann zeta function. Solutions to Landau's problem with…
According to a conjecture attributed to Polya and Hilbert, there is a self-adjoint operator whose eigenvalues are the the nontrivial zeros of the Riemann zeta function. We show that the near-horizon dynamics of a massive scalar field in the…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian…
We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of…
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one…
Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Using tensor network methods, we simulate the real-time evolution of the lattice Thirring model quenched out of equilibrium in both the critical and massive phases and study the appearance of dynamical quantum phase transitions, as…
We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The…
We transform the counting function for the Riemann zeros into a Korringa-Kohn-Rostoker (KKR) determinant, assisted by Krein's theorem. This is based on our observation that the function derived from a few methods can all be recast into two…
This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is…
The non-trivial zeros of the Riemann zeta function and the prime numbers can be plotted by a modified von Mangoldt function. The series of non-trivial zeta zeros and prime numbers can be given explicitly by superposition of harmonic waves.…
In this paper, we present a proof of the Riemann hypothesis. We show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
The unknown parameters of the recently-proposed (Int J. Geom. Meth. Mod. Phys. 1, 751 [2004]) Castro-Mahecha model of the imaginary parts (lambda_{j}) of the nontrivial Riemann zeros are the phases (alpha_{k}) and the frequency parameter…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
We consider the Rabi Hamiltonian which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition…