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In this work a nonlinear evolution of pure states of a finite dimensional quantum system is introduced, in particular a Riccati evolution equation.
It is shown how this class of dynamics is actually a Hamiltonian dynamics in the complex projective space.
In this projective space it is shown that there is a nonlinear superposition rule, consistent with its linear counterpart in the Hilbert space. As an example, the developed nonlinear formalism is applied to the semiclassical Jaynes–Cummings model.
Later, it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states.
To show this, the fact that in quantum mechanics it is possible to immerse a ''classical'' manifold into the Hilbert space is employed, such that one may parametrize the time-dependence of the wave function through the variation of parameters in the classical manifold.
The immersion allows to consider the so-called principle of analogy, i.e. using the procedures and structures available from the classical setting to employ them in the quantum setting.
Finally, it is introduced the contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and it is showed that it is a natural candidate for a geometric description of non-dissipative and dissipative systems.
Envy, the inclination to compare rewards, can be expected to unfold when inequalities in terms of pay-off differences are generated in competitive societies. It is shown that increasing levels of envy lead inevitably to a self-induced separation into a lower and an upper class. Class stratification is Nash stable and strict, with members of the same class receiving identical rewards. Upper-class agents play exclusively pure strategies, all lower-class agents the same mixed strategy. The fraction of upper-class agents decreases progressively with larger levels of envy, until a single upper-class agent is left. Numerical simulations and a complete analytic treatment of a basic reference model, the shopping trouble model, are presented. The properties of the class-stratified society are universal and only indirectly controllable through the underlying utility function, which implies that class-stratified societies are intrinsically resistant to political control. Implications for human societies are discussed. It is pointed out that the repercussions of envy are amplified when societies become increasingly competitive.
Direct nanoscopic observation of plasma waves in the channel of a graphene field-effect transistor
(2020)
Plasma waves play an important role in many solid-state phenomena and devices. They also become significant in electronic device structures as the operation frequencies of these devices increase. A prominent example is field-effect transistors (FETs), that witness increased attention for application as rectifying detectors and mixers of electromagnetic waves at gigahertz and terahertz frequencies, where they exhibit very good sensitivity even high above the cut-off frequency defined by the carrier transit time. Transport theory predicts that the coupling of radiation at THz frequencies into the channel of an antenna-coupled FET leads to the development of a gated plasma wave, collectively involving the charge carriers of both the two-dimensional electron gas and the gate electrode. In this paper, we present the first direct visualization of these waves. Employing graphene FETs containing a buried gate electrode, we utilize near-field THz nanoscopy at room temperature to directly probe the envelope function of the electric field amplitude on the exposed graphene sheet and the neighboring antenna regions. Mapping of the field distribution documents that wave injection is unidirectional from the source side since the oscillating electrical potentials on the gate and drain are equalized by capacitive shunting. The plasma waves, excited at 2 THz, are overdamped, and their decay time lies in the range of 25-70 fs. Despite this short decay time, the decay length is rather long, i.e., 0.3-0.5 μm, because of the rather large propagation speed of the plasma waves, which is found to lie in the range of 3.5-7 × 106 m/s, in good agreement with theory. The propagation speed depends only weakly on the gate voltage swing and is consistent with the theoretically predicted 1/4 power law.
A central motivation for the development of x-ray free-electron lasers has been the prospect of time-resolved single-molecule imaging with atomic resolution. Here, we show that x-ray photoelectron diffraction—where a photoelectron emitted after x-ray absorption illuminates the molecular structure from within—can be used to image the increase of the internuclear distance during the x-ray-induced fragmentation of an O2 molecule. By measuring the molecular-frame photoelectron emission patterns for a two-photon sequential K-shell ionization in coincidence with the fragment ions, and by sorting the data as a function of the measured kinetic energy release, we can resolve the elongation of the molecular bond by approximately 1.2 a.u. within the duration of the x-ray pulse. The experiment paves the road toward time-resolved pump-probe photoelectron diffraction imaging at high-repetition-rate x-ray free-electron lasers.
We study D and DS mesons at finite temperature using an effective field theory based on chiral and heavy-quark spin-flavor symmetries within the imaginary-time formalism. Interactions with the light degrees of freedom are unitarized via a Bethe-Salpeter approach, and the D and self-energies are calculated self-consistently. We generate dynamically the e D∗0(2300)and Ds(2317)state, and study their possible identification as the chiral We study Dand Dsmesons at finite temperature using an effective field theory based on chiral and heavy-quark spin-flavor symmetries within the imaginary-time formalism. Interactions with the light degrees of freedom are unitarized via a Bethe-Salpeter approach, and the Dand Dsself-energies are calculated self-consistently. We generate dynamically the D∗0(2300)and Ds(2317)states, and study their possible identification as the chiral partners of the Dand Dsground states, respectively. We show the evolution of their masses and decay widths as functions of temperature, and provide an analysis of the chiral-symmetry restoration in the heavy-flavor sector below the transition temperature. In particular, we analyse the very special case of the D-meson, for which the chiral partner is associated to the double-pole structure of the D∗0(2300).
he Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the most difficult to implement in many-fermion systems, which are common in nuclear physics. To investigate the consequences of ignoring the PEP, we discuss several algebraic models in nuclear structure physics, in particular cluster models. Sometimes they tend to ignore the Pauli Exclusion Principle for practical reasons, leading to flawed interpretations. Though at first sight there seems to be an agreement to experiment, often it is due to the limited number of states known experimentally. We discuss several models which include or not the PEP, illustrating through their differences the importance of the PEP. This contribution is also a review of recently published results.
First, we propose a scale-invariant modified gravity interacting with a neutral scalar inflaton and a Higgs-like SU(2)×U(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes, in the physical Einstein frame, a quintessential inflationary scenario driven by the “inflaton” together with the gravity-“inflaton” assisted dynamical spontaneous SU(2)×U(1) symmetry breaking in the post-inflationary universe, whereas the SU(2)×U(1) symmetry remains intact in the inflationary epoch. Next, we find the explicit representation of the latter quintessential inflationary model with a dynamical Higgs effect as an Eddington-type purely affine gravity.
High-quality single crystals of the unconventional superconductor NdFeAsO1 − xFx were grown. We developed a new optimized flux technique to overcome the difficulties in single-crystal growth and the sample quality limitations of NdFeAsO1 − xFx. The normal state of the F-doped samples exhibits simple metallic behavior upon cooling down from room temperature, followed by a sharp superconducting transition. The values of residual resistivity ratio (RRR) is 3.2, 6.4, and 10.3 for x = 0.1, 0.15, and 0.2, respectively. Both the large RRR and the narrow superconducting transition signpost the high quality of the crystals. We have examined the in- and out-of-plane lower critical fields, and the field at which vortices penetrate the sample of NdFeAsO1 − xFx (x = 0.1). The anisotropy ratio [γHc1 (0)] increased slightly with increasing temperature from 0.8 Tc to Tc. The temperature dependence of the first vortex penetration field was obtained under the static magnetic field, H, parallel to the c- and ab- axis, and pronounced changes in the Hc1(T) curvature were observed, which are attributed to the multi-band superconductivity.
The production of light (anti-)(hyper-)nuclei in heavy-ion collisions at the LHC is considered in the framework of the Saha equation, making use of the analogy between the evolution of the early universe after the Big Bang and that of “Little Bangs” created in the lab. Assuming that disintegration and regeneration reactions involving light nuclei proceed in relative chemical equilibrium after the chemical freeze-out of hadrons, their abundances are determined through the famous cosmological Saha equation of primordial nucleosynthesis and show no exponential dependence on the temperature typical for the thermal model. A quantitative analysis, performed using the hadron resonance gas model in partial chemical equilibrium, shows agreement with experimental data of the ALICE collaboration on d, 3He, HΛ3, and 4He yields for a very broad range of temperatures at T≲155 MeV. The presented picture is supported by the observed suppression of resonance yields in central Pb–Pb collisions at the LHC. Keywords: Light (anti-)(hyper-)nuclei production, Saha equation, Partial chemical equilibrium.
Rethinking superdeterminism
(2020)
Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical description of the measurement process. This “measurement problem” indicates that quantum mechanics is at least an incomplete theory—good as far as it goes, but missing a piece—or, more radically, is in need of complete overhaul. Here we describe an approach which may provide this sought-for completion or replacement: Superdeterminism. A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent non-locality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way.
The third dataset dedicated to the Open Guided Waves platform aims at carbon fiber composite plates with an additional omega stringer at constant temperature conditions. The two structures used in this work are representative for real aircraft components. Comprehensive measurements were recorded in order to study (I) the impact of the omega stringer on guided wave propagation, and (II) elliptical reference damages of different sizes located at three separate positions on the structure. Measurements were recorded for narrowband excitation (5-cycle toneburst with varying carrier frequencies) and broadband excitation (using chirp waveforms). The paper presents the results of a technical validation including numerical modelling, and enables further research, for example related to probability of detection (POD) analysis.
In power systems, flow allocation (FA) methods enable to allocate the usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator-specific or producer-specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBEs), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDFs). Despite their intuitive and computationally efficient concepts, they are restricted to networks with passive transmission elements only. As soon as a significant number of controllable transmission elements, such as high-voltage direct current (HVDC) lines, operate in the system, they lose their applicability. This work reformulates the two methods in terms of Virtual Injection Patterns (VIPs), which allows one to efficiently introduce a shift parameter q to tune contributions of net sources and net sinks in the network. In this work, major properties and differences in the methods are pointed out, and it is shown how the MP and EBE algorithms can be applied to generic meshed AC-DC electricity grids: by introducing a pseudo-impedance ω¯ , which reflects the operational state of controllable elements and allows one to extend the PTDF matrix under the assumption of knowing the current flow in the system. Basic properties from graph theory are used to solve for the pseudo-impedance in dependence of the position within the network. This directly enables, e.g., HVDC lines to be considered in the MP and EBE algorithms. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of 181 nodes and an 18% transmission expansion compared to today’s total transmission capacity volume. The allocations of MP and EBE show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion, a method of distributing operational and capital expenditures is proposed. In addition, it is shown how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.
We study the influence of the baryon chemical potential μB on the properties of the Quark–Gluon–Plasma (QGP) in and out-of equilibrium. The description of the QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature Tc from lattice Quantum Chromodynamics (QCD). We study the transport coefficients such as the ratio of shear viscosity η and bulk viscosity ζ over entropy density s, i.e., η/s and ζ/s in the (T,μ) plane and compare to other model results available at μB=0 . The out-of equilibrium study of the QGP is performed within the Parton–Hadron–String Dynamics (PHSD) transport approach extended in the partonic sector by explicitly calculating the total and differential partonic scattering cross sections based on the DQPM and the evaluated at actual temperature T and baryon chemical potential μB in each individual space-time cell where partonic scattering takes place. The traces of their μB dependences are investigated in different observables for symmetric Au + Au and asymmetric Cu + Au collisions such as rapidity and mT -distributions and directed and elliptic flow coefficients v1,v2 in the energy range 7.7 GeV ≤sNN−−−−√≤200 GeV.
An incoming or outgoing hadron in a hard collision with large momentum transfer gets squeezed in the transverse direction to its momentum. In the case of nuclear targets, this leads to the reduced interaction of such hadrons with surrounding nucleons which is known as color transparency (CT). The identification of CT in exclusive processes on nuclear targets is of significant interest not only by itself but also due to the fact that CT is a necessary condition for the applicability of factorization for the description of the corresponding elementary process. In this paper we discuss the semiexclusive processes A(e,e′π+) , A(π−,l−l+) and A(γ,π−p) . Since CT is closely related to hadron formation mechanism, the reduced interaction of ’pre-hadrons’ with nucleons is a common feature of generic high-energy inclusive processes on nuclear targets, such as hadron attenuation in deep inelastic scattering (DIS). We will discuss the novel way to study hadron formation via slow neutron production induced by a hard photon interaction with a nucleus. Finally, the opportunity to study hadron formation effects in heavy-ion collisions in the NICA regime will be considered.
For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μI≥mπ/2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).