Related papers: Plane Pendulum and Beyond by Phase Space Geometry
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically-relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically…
In collider physics, the properties of hadronic jets are often measured as a function of their lab-frame momenta. However, jet fragmentation must occur in a particular rest frame defined by all color-connected particles. Since this frame…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
To understand spacetime dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate…
A satisfactory theory of quantum gravity may necessitate a drastic modification of our perception of space-time, by giving it a foamy structure at distances comparable to the Planck length. It is argued in this essay that the experimental…
We discuss phenomenology of extra time dimensions in a scenario where the standard model particles are localized in ``our'' time, whereas gravity can propagate in all time dimensions. For an odd number of extra times, at small distances,…
Quantum entanglement is affected by unitary evolution, which spreads the entanglement through the whole system, and also by measurements, which usually tends to disentangle subsystems from the rest. Their competition has been known to…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction.…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
In a Quantum Field Theory with a time-dependent background, time-translational symmetry is broken. We therefore expect time-dependent loop corrections to cosmological observables after renormalization for an interacting field, with the…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that…
The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism…
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…
The problem of determining the underlying dynamics of a system when only given data of its state over time has challenged scientists for decades. In this paper, the approach of using machine learning to model the updates of the phase space…