Quantum Mechanical Fluctuations Research Articles

Stability Analysis, Modulation Instability, and Beta-Time Fractional Exact Soliton Solutions to the Van der Waals Equation

The study consists of the distinct types of the exact soliton solutions to an important model called the beta-time fractional (1 + 1)-dimensional non-linear Van der Waals equation. This model is used to explain the motion of molecules and materials. The Van der Waals equation explains the phase separation phenomenon. Noncovalent Van der Waals or dispersion forces usually have an effect on the structure, dynamics, stability, and function of molecules and materials in different branches of science, including biology, chemistry, materials science, and physics. Solutions are obtained, including dark, dark-singular, periodic wave, singular wave, and many more exact wave solutions by using the modified extended tanh function method. Using the fractional derivatives makes different solutions different from the existing solutions. The gained results will be of high importance in the interaction of quantum-mechanical fluctuations, granular matters, and other applications of the Van der Waals equation. The solutions may be useful in distinct fields of science and civil engineering, as well as some basic physical ones like those studied in geophysics. The results are verified and represented by two-dimensional, three-dimensional, and contour graphs by using Mathematica software. The obtained results are newer than the existing results. Stability analysis is also performed to check the stability of the concerned model. Furthermore, modulation instability is studied to study the stationary solutions of the concerned model. The results will be helpful in future studies of the concerned system. In the end, we can say that the method used is straightforward and dynamic, and it will be a useful tool for debating tough issues in a wide range of fields.

Electron scattering beyond the independent atom model: Quantum fluctuation of the Coulomb potential.

In the past century, electron scattering has mostly served as a powerful tool to measure the microscopic structure of gases, liquids, and solids in either a static or time-resolved manner. One common basis for these works is the independent atom model, which directly relates electron scattering signals to the atomic structure of matter. In this perspective, we explore the information content of electron scattering that goes beyond the independent atom model. We show that the small-angle limit of the electron scattering signal encodes the quantum mechanical fluctuation of the long-range Coulomb potential. This quantum fluctuation, described by the second moment of the dipole operator, is the root cause of the intermolecular van der Waals forces.

The nonlinear wave dynamics of the space-time fractional van der Waals equation via three analytical methods

In this paper, we explore the new exact soliton solutions of the truncated M-fractional nonlinear (1 + 1)-dimensional van der Waals equation by applying the expa function method, extended (G′/G)-expansion method, and modified simplest equation method. The concerned equation is a challenging problem in the modeling of molecules and materials. Noncovalent van der Waals or dispersion forces are frequent and have an impact on the structure, dynamics, stability, and function of molecules and materials in biology, chemistry, materials science, and physics. The results obtained are verified and represented by two-dimensional, three-dimensional, and contour graphs. These results are newer than the existing results in the literature due to the use of fractional derivative. The achieved solutions will be of high significance in the interaction of quantum-mechanical fluctuations, granular matter, and other areas of van der Waals equation applications. Therefore, the obtained solutions are valuable for future studies of this model.

On the Van der Waals model on granular matters with truncated M-fractional derivative

In this work, exact solutions of the Van der Waals model (vdWm) are investigated with a new algebraic analytical method. The closed-form analysis of the vdW equation arising in the context of the fluidized granular matter is implemented under the effect of time-fractional M-derivative. The vdWm is a challenging problem in the modelling of molecules and materials. Noncovalent Van der Waals or dispersion forces are frequent and have an impact on the structure, dynamics, stability, and function of molecules and materials in biology, chemistry, materials science and physics. The auxiliary equation which is known as a direct analytical method is constructed for the nonlinear fractional equation. The process includes a transformation based on Weierstrass and Jacobi elliptic functions. Wave solutions of the model are analytically verified for the various cases. Then, graphical patterns are presented to show the physical explanation of the model interactions. The achieved solutions will be of high significance in the interaction of quantum-mechanical fluctuations, granular matter and other areas of vdWm applications.

Quantum origins of scalar gravitational waves: Exploring the conformal factor in scalar–tensor theory of gravity

Delving into the realm of scalar–tensor theory of gravity, this paper uncovers the intricate details of the conformal factor and its correspondence to quantum mechanical mass fluctuations. Shedding light on the theory’s key findings, we explore the quantum mechanical nature of the wave equation associated with mass fluctuations, predicting the creation of scalar gravitational waves. The association of conformal fluctuations with the quantum potential presents a remarkable feature of this theory, which predicts a scalar component of gravitational waves. With the potential to generate such waves in a laboratory set-up, this theory invites exciting possibilities for empirical testing, highlighting the quantum mechanical origin of scalar gravitational waves.

The scaling of primordial gauge fields

The large-scale magnetic fields arising from the quantum mechanical fluctuations of the hypercharge are investigated when the evolution of the gauge coupling is combined with a sufficiently long inflationary stage. In this framework the travelling waves associated with the quantum mechanical initial conditions turn asymptotically into standing waves which are the gauge analog of the Sakharov oscillations. Even if the rate of dilution of the hypermagnetic and hyperelectric fields seems to be superficially smaller than expected from the covariant conservation of the energy-momentum tensor, the standard evolution for wavelengths larger than the Hubble radius fully accounts for this anomalous scaling which is anyway unable to increase the amplitude of the magnetic power spectra after symmetry breaking. An effective amplification of the gauge power spectra may instead occur when the post-inflationary expansion rate is slower than radiation. We stress that the modulations of the gauge power spectra freeze as soon as the relevant wavelengths reenter the Hubble radius and not at the end of inflation. After the Mpc scale crosses the comoving Hubble radius the scaling of the magnetic power spectrum follows from the dominance of the conductivity. From these two observations the late-time values of the magnetic power spectra are accurately computed in the case of a nearly scale-invariant slope and contrasted with the situation where the phases of Sakharov oscillations are not evaluated at horizon crossing but at the end of inflation, i.e. when all the wavelengths relevant for magnetogenesis are still larger than the comoving horizon.

Noise dynamics of quantum annealers: estimating the effective noise using idle qubits

Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc. have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.

Mapping state transition susceptibility in quantum annealing

Quantum annealing is a novel type of analog computation that aims to use quantum-mechanical fluctuations to search for optimal solutions for Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave devices, works by applying a time-dependent transverse field, which puts all qubits into a uniform state of superposition, and then applying a Hamiltonian over time, which describes a user-programed Ising problem. We present a method that utilizes two control features of D-Wave quantum annealers, namely reverse annealing and an $h$-gain schedule, to quantify the susceptibility, or the distance, between two classical states of an Ising problem. The starting state is encoded using reverse annealing, and the second state is encoded on the linear terms of a problem Hamiltonian. An $h$-gain schedule is specified, which incrementally increases the strength of the linear terms, thus allowing a quantification of the $h$-gain strength required to transition the anneal into a specific state at the final measurement. Because of the nature of quantum annealing, the state tends towards global minima, and therefore we restrict the second classical state to a minimum solution of the given Ising problem. This susceptibility mapping, when enumerated across all initial states, shows in detail the behavior of the quantum annealer during reverse annealing. The procedure is experimentally demonstrated on three small test Ising models which were embedded in parallel on the D-Wave Advantage_system4.1. Analysis of the state transition mapping shows detailed characteristics of the reverse annealing process, including intermediate state transition paths, which are visually represented as state transition networks.

Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much larger than the average intergalaxy separation, implying that they lie in the same universality class. We also show that the distribution of galaxies is a highly correlated disordered system (relative to the uncorrelated Poisson distribution), as measured by the τ order metric. Finally, we consider the ability of large-scale clustering statistics to constrain cosmological parameters, such as the Universe’s expansion rate, using simulation-based inference. Both the nearest-neighbor distribution and pair-connectedness function (which includes contributions from correlation functions of all order) are found to considerably tighten bounds on the amplitude of quantum-mechanical fluctuations from inflation at a level equivalent to observing 25 times more galaxies. The pair-connectedness function in particular provides a useful alternative to the standard three-particle correlation, since it contains similar large-scale information to the three-point function, can be computed highly efficiently, and can be straightforwardly extended to small scales (though likely requires simulation-based modeling). This work provides the first application of such techniques to cosmology, providing both a novel system to test heterogeneous media descriptors and a tranche of new tools for cosmological analyses. A range of extensions are possible, including implementation on observational data; this will require further study on various observational effects, necessitating high-resolution simulations.6 MoreReceived 16 July 2022Revised 2 January 2023Accepted 10 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011038Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLarge scale structure of the UniverseGravitation, Cosmology & AstrophysicsInterdisciplinary Physics

Tilted spatially nonflat inflation

We construct nonlinear inflaton potential-energy densities that describe not necessarily very slowly rolling closed and open inflation models, and compute tilted primordial spatial inhomogeneity power spectra that follow from quantum-mechanical fluctuations during inflation in these models. Earlier nonflat inflation model power spectra computations assumed an inflaton potential-energy density with a linear slope that resulted in very slow roll during inflation and untilted power spectra. These new tilted power spectra differ from those that have previously been used to study cosmological data in nonflat cosmological models.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Tex. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Expansion dynamics in two-dimensional Bose-Hubbard lattices: Bose-Einstein condensate and thermal cloud

We study the temporal expansion of an ultracold Bose gas in two-dimensional square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical [Bose-Einstein condensate (BEC)] part and quantum mechanical fluctuations. After a quench, i.e., after a sudden switch of the lattice nearest-neighbor hopping, the expanding bosonic cloud separates spatially into a fast ballistic forerunner and a slowly expanding central part controlled by self-trapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.

Quantum-critical scale invariance in a transition metal alloy

Quantum-mechanical fluctuations between competing phases induce exotic collective excitations that exhibit anomalous behavior in transport and thermodynamic properties, and are often intimately linked to the appearance of unconventional Cooper pairing. High-temperature superconductivity, however, makes it difficult to assess the role of quantum-critical fluctuations in shaping anomalous finite-temperature physical properties. Here we report temperature-field scale invariance of non-Fermi liquid thermodynamic, transport, and Hall quantities in a non-superconducting iron-pnictide, Ba(Fe1/3Co1/3Ni1/3)2As2, indicative of quantum criticality at zero temperature and applied magnetic field. Beyond a linear-in-temperature resistivity, the hallmark signature of strong quasiparticle scattering, we find a scattering rate that obeys a universal scaling relation between temperature and applied magnetic fields down to the lowest energy scales. Together with the dominance of hole-like carriers close to the zero-temperature and zero-field limits, the scale invariance, isotropic field response, and lack of applied pressure sensitivity suggests a unique quantum critical system unhindered by a pairing instability.

Maximal-entropy initial state of the Universe as a microscopic description of inflation

We propose that the initial state of the Universe was an isotropic state of maximal entropy. Such a state can be described in terms of a state of closed, interacting, fundamental strings in their high-temperature Hagedorn phase. The entropy density in this state is equal to the square root of the energy density in Planck units, while the pressure is positive and equal to the energy density. These relations imply a maximally large entropy density and, therefore, a state that cannot be described by a semiclassical spacetime geometry. If one nevertheless insists on an effective semiclassical description of this state, she can do so by ignoring the entropy. This leads to a partially equivalent description in which the pressure appears to be negative and equal in magnitude to the energy density, as if the energy-momentum tensor was that of a cosmological constant. From this effective perspective, the state describes a period of string-scale inflation. The bound state of strings ultimately decays, possibly by a process akin to Hawking radiation, and undergoes a transition into a phase of hot radiation. But, from the effective perspective, the same decay corresponds to the heating of the Universe at the end of inflation. Small quantum mechanical fluctuations in the initial state lead to scale-invariant temperature anisotropies in the hot radiation. The temperature anisotropies are interpreted in the effective description as arising from quantum fluctuations of the curvature and an effective inflaton field. The stringy microscopic description determines the parameters of the model of inflation, as well as the cosmological observables, in terms of the string length scale and coupling strength. Our framework is similar, conceptually, to a recent description of black holes in terms of a maximal entropy state of strings in the Hagedorn phase.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations.

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Modeling Cosmic Expansion, and Possible Inflation, as a Thermodynamic Heat Engine

Abstract Assuming a closed universe with slight positive curvature, cosmic expansion can be modeled as a heat engine where we define the “system,” collectively, as those regions of space within the observable universe, which will later evolve into voids. We identify the “surroundings,” collectively, as those pockets of space that will eventually develop into matter-filled galaxies, clusters, superclusters, and filament walls. Using this model, we can find the energy needed for cosmic expansion using basic thermodynamic principles and show that cosmic expansion had as its origin a finite initial energy density, pressure, volume, and temperature. Inflation in the traditional sense, with the inflaton field, may also not be required. We also argue that homogeneities and inhomogeneities in the WMAP temperature profile are attributable to quantum mechanical fluctuations about a fixed background temperature in the initial isothermal expansion phase of the cycle, which we identify with inflation. Fluctuations in temperature can cause certain regions of space to lose heat while other regions will absorb that heat. The voids, being those regions that absorb the heat, will expand, thereby leaving slightly cooler temperatures for the surroundings, where matter will later congregate. Upon freeze-out, this could produce the observed WMAP signature with its associated inhomogeneity. Finally, using the uncertainty relation, we estimate that the temperature and time for formation of WMAP inhomogeneities occurred at roughly 3.02 × 1027 K and 2.54 × 10−35 s, respectively, after first initiation of volume expansion. This is in line with current estimates for the end of the inflationary epoch. The heat input in the inflationary phase is calculated as roughly Q = 1.81 × 1094 J (photons only); the collective void volume increases by a factor of only 5.65. The bubble voids in the observable universe increase in size from about 0.046 to 0.262 m3 within this inflationary period in our model.

Theoretical Comparison of Noise Characteristics in Semiconductor and Fiber Optical Amplifiers

Characteristics of the intensity noise, the phase noise, the frequency noise, and the spectral linewidth in the semiconductor optical amplifier (SOA) and the erbium doped fiber amplifier (EDFA) were theoretically examined with a unified analyzing manner. Quantum mechanical fluctuations associating with the optical amplification and the spontaneous emission were taken into account as noise sources on the traveling optical wave. Quantitative calculated results are obtained. As general features, the SOA reveals higher noise than the EDFA, due to larger inclusion of the amplified spontaneous emission, larger value of the optical absorption and larger fluctuation of the injected electron density. However, the SOA has an exceptional feature to suppress the relative intensity noise (RIN) of the output light below the input RIN level under suitable operating condition. The spectrum linewidth hardly increases in both the SOA and the EDFA under linear operation.

Solvent fluctuations and nuclear quantum effects modulate the molecular hyperpolarizability of water

Second-Harmonic Scatteringh (SHS) experiments provide a unique approach to probe non-centrosymmetric environments in aqueous media, from bulk solutions to interfaces, living cells and tissue. A central assumption made in analyzing SHS experiments is that the each molecule scatters light according to a constant molecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, we investigate the dependence of the molecular hyperpolarizability of water on its environment and internal geometric distortions, in order to test the hypothesis of constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculations of the hyperpolarizability of a molecule embedded in point-charge environments obtained from simulations of bulk water. We demonstrate that both the heterogeneity of the solvent configurations and the quantum mechanical fluctuations of the molecular geometry introduce large variations in the non-linear optical response of water. This finding has the potential to change the way SHS experiments are interpreted: in particular, isotopic differences between H$_2$O and D$_2$O could explain recent second-harmonic scattering observations. Finally, we show that a simple machine-learning framework can predict accurately the fluctuations of the molecular hyperpolarizability. This model accounts for the microscopic inhomogeneity of the solvent and represents a first step towards quantitative modelling of SHS experiments.

Low temperature diffusivity of self-interstitial defects in tungsten

The low temperature diffusivity of nanoscale crystal defects, where quantum mechanical fluctuations are known to play a crucial role, are essential to interpret observations of irradiated microstructures conducted at cryogenic temperatures. Using density functional theory calculations, quantum heat bath molecular dynamics and open quantum systems theory, we evaluate the low temperature diffusivity of self-interstitial atom clusters in tungsten valid down to temperatures of 1 K. Due to an exceptionally low defect migration barrier, our results show that interstitial defects exhibit very high diffusivity of order over the entire range of temperatures investigated.

Cumulants and nonlinear response of high pT harmonic flow at sNN=5.02 TeV

Event-by-event fluctuations caused by quantum mechanical fluctuations in the wave function of colliding nuclei in ultrarelativistic heavy ion collisions were recently shown to be necessary for the simultaneous description of $R_{AA}$ as well as the elliptic and triangular flow harmonics at high $p_T$ in PbPb collisions at the Large Hadron Collider. In fact, the presence of a finite triangular flow as well as cumulants of the flow harmonic distribution that differ from the mean are only possible when these event-by-event fluctuations are considered. In this paper we combine event-by-event viscous hydrodynamics and jet quenching to make predictions for high $p_T$ $R_{AA}$, $v_2\{2\}$, $v_3\{2\}$, and $v_2\{4\}$ in PbPb collisions at $\sqrt{s_{NN}}=5.02$ TeV. With an order of magnitude larger statistics we find that high $p_T$ elliptic flow does not scale linearly with the soft elliptical flow, as originally thought, but has deviations from perfectly linear scaling. A new experimental observable, which involves the difference between the ratio of harmonic flow cumulants at high and low $p_T$, is proposed to investigate the fluctuations of high $p_T$ flow harmonics and measure this nonlinear response. By varying the path length dependence of the energy loss and the viscosity of the evolving medium we find that $R_{AA}(p_T)$ and $v_2\{2\}(p_T)$ strongly depend on the choice for the path length dependence of the energy loss, which can be constrained using the new LHC run 2 data.