scholarly journals A LUTTINGER LIQUID CORE INSIDE HELIUM-4 FILLED NANOPORES

2012 ◽  
Vol 26 (22) ◽  
pp. 1244002 ◽  
Author(s):  
ADRIAN DEL MAESTRO
Keyword(s):  
Quantum Monte Carlo ◽  
Large Scale ◽  
Liquid Core ◽  
Luttinger Liquid ◽  
Three Dimensions ◽  
Dimensional System ◽  
Hydrodynamic Description ◽  
One Dimensional ◽  
Helium 4 ◽  
State Of Matter

As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

On the Recovery of 3D Spatial Statistics of Particles from 1D Measurements: Implications for Airborne Instruments

2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner
Keyword(s):  
Point Processes ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
Cloud Droplets ◽  
Sampling Variability ◽  
One Dimensional ◽  
Natural Sampling ◽  
The One

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.

INSTANTONS AND SPHALERONS IN SKYRMED WEINBERG–SALAM MODELS AND GRASSMANNIAN MODELS

2000 ◽  
Vol 15 (02) ◽  
pp. 251-264
Author(s):  
F. BRAU ◽  
V. BRIHAYE ◽  
D. H. TCHRAKIAN
Keyword(s):  
Higgs Doublet ◽  
Three Dimensions ◽  
Dimensional System ◽  
One Dimensional ◽  
Yang Mills ◽  
Pure Gauge ◽  
Static Solutions ◽  
The One ◽  
Matter Fields

Several Lagrangians describing the SU(2) Yang–Mills (YM) field interacting with matter are considered, which support both instantons (in four Euclidean dimensions) and sphaleron (in three dimensions, static) solutions. The matter fields are the complex Higgs doublet for the Weinberg–Salam (WS) model, and a (2 × 4) Grassmannian model. These Lagrangians feature Skyrme-like extensions to enable the existence of the instantons, which decay as pure gauge at infinity. For two of these models, we have numerically integrated the one-dimensional system arising from the imposition of radial ansatz.

scholarly journals Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors

2019 ◽  
Vol 881 ◽  
pp. 384-419 ◽  
Author(s):  
Sandeep R. Murthy ◽  
Taraneh Sayadi ◽  
Vincent Le Chenadec ◽  
Peter J. Schmid ◽  
Daniel J. Bodony
Keyword(s):  
Heat Source ◽  
Modal Analysis ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Harmonic Excitation ◽  
Finite Amplitude ◽  
Dimensional System ◽  
Acoustic Oscillations ◽  
Strong Response ◽  
One Dimensional

A simplified model is introduced to study finite-amplitude thermo-acoustic oscillations in $N$-periodic annular combustion devices. Such oscillations yield undesirable effects and can be triggered by a positive feedback between heat-release and pressure fluctuations. The proposed model, comprising the governing equations linearized in the acoustic limit, and with each burner modelled as a one-dimensional system with acoustic damping and a compact heat source, is used to study the instability caused by cross-sector coupling. The coupling between the sectors is included by solving the one-dimensional acoustic jump conditions at the locations where the burners are coupled to the annular chambers of the combustion device. The analysis takes advantage of the block-circulant structure of the underlying stability equations to develop an efficient methodology to describe the onset of azimuthally synchronized motion. A modal analysis reveals the dominance of global instabilities (encompassing the large-scale dynamics of the entire system), while a non-modal analysis reveals a strong response to harmonic excitation at forcing frequencies far from the eigenfrequencies, when the overall system is linearly stable. In all presented cases, large-scale, azimuthally synchronized (coupled) motion is observed. The relevance of the non-modal response is further emphasized by demonstrating the subcritical nature of the system’s Hopf point via an asymptotic expansion of a nonlinear model representing the compact heat source within each burner.

scholarly journals Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

2018 ◽  
Vol 175 ◽  
pp. 03007 ◽  
Author(s):  
Andrew C. Loheac ◽  
Jens Braun ◽  
Joaquín E. Drut
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Three Dimensions ◽  
Strong Coupling Regime ◽  
Dimensional System ◽  
Perturbative Calculations ◽  
One Dimensional ◽  
Unitary Fermi Gas ◽  
Lattice Perturbation Theory ◽  
Lattice Perturbation

We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick’s theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.

World-structure and non-Euclidean honeycombs

1950 ◽  
Vol 201 (1066) ◽  
pp. 417-437 ◽  
Keyword(s):  
Hyperbolic Space ◽  
Special Theory ◽  
Point Of View ◽  
Three Dimensions ◽  
Dimensional System ◽  
Theory Of Relativity ◽  
Point Distribution ◽  
One Dimensional ◽  
Generating Relations ◽  
Integral Solutions

Milne (1934) described a one-dimensional system of discrete particles in uniform relative motion such that the aspect of the whole system is the same from each particle. The purpose of the present paper is to construct analogous systems in two and three dimensions. If the uniformly moving observers regraduate their clocks so as to describe each other as relatively stationary, the private Euclidean spaces of the Special Theory of Relativity become public hyperbolic space. This point of view leads to a discussion of uniform honeycombs in hyperbolic space, four of which were discovered by Schlegel (1883, p. 444). One of the new honeycombs, called {4, 4, 3}, has for its vertices the points whose four co-ordinates are proportional to the integral solutions of the Diophantine equation t 2 - x 2 - y 2 - z 2 = 1. As a by-product, a simple set of generators and generating relations are obtained for the group of all integral Lorentz transformations (Schild 1949, p. 39). Another by-product is the enumeration of those groups generated by reflexions in hyperbolic space whose fundamental regions are tetrahedra of finite volume. The work culminates in the discovery of a point-distribution whose mesh is seven times as close as that of {4, 4, 3}, though apparently still far too coarse to be of direct cosmological significance. It follows that some irregularity in the distribution of the extragalactic nebulae is almost certainly geometrically inevitable.

scholarly journals Fluctuation-generated Plasma Oscillations

1975 ◽  
Vol 28 (3) ◽  
pp. 283
Author(s):  
AZ Tirkel ◽  
JLA Francey ◽  
GJ Troup
Keyword(s):  
Magnetic Fields ◽  
Three Dimensions ◽  
Dimensional System ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Plasma Oscillations ◽  
One Dimensional ◽  
Longitudinal Modes ◽  
Basic Equations

A theory of spontaneous plasma oscillations is developed from basic equations. Longitudinal modes in a one-dimensional system are presented in detail, while possible extensions to three dimensions and the effects of external magnetic fields are indicated. The basic equations lead to a Van der Pol equation. Similarities are noted between plasmas and two-level lasers.

New Models of Content Creation and Scholarship at the Intersection of Library Spaces, Technologies, and Expertise

2018 ◽  
Author(s):  
Mike Nutt ◽  
Gregory Raschke
Keyword(s):  
Large Scale ◽  
Interactive Media ◽  
Scholarly Communication ◽  
Three Dimensions ◽  
Organizational Capabilities ◽  
High Definition ◽  
Content Creation ◽  
Full Life Cycle ◽  
Digital Scholarship ◽  
Digital Objects

Library spaces that blend collaboration areas, advanced technologies, and librarian expertise are creating new modes of scholarly communication. These spaces enable scholarship created within high-definition, large-scale visual collaborative environments. This emergent model of scholarly communication can be experienced within those specific contexts or through digital surrogates on the networked Web. From experiencing in three dimensions the sermons of John Donne in 1622 to interactive media interpretations of American wars, scholars are partnering with libraries to create immersive digital scholarship. Viewing the library as a research platform for these emergent forms of digital scholarship presents several opportunities and challenges. Opportunities include re-engaging faculty in the use of library space, integrating the full life-cycle of the research enterprise, and engaging broad communities in the changing nature of digitally-driven scholarship. Issues such as identifying and filtering collaborations, strategically managing staff resources, creating surrogates of immersive digital scholarship, and preserving this content for the future present an array of challenges for libraries that require coordination across organizations. From engaging and using high-technology spaces to documenting the data and digital objects created, this developing scholarly communication medium brings to bear the multifaceted skills and organizational capabilities of libraries.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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