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

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.

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Topological correlators and surface defects from equivariant cohomology

Journal of High Energy Physics ◽

10.1007/jhep09(2020)185 ◽

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.

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Automated lattice perturbation theory and relativistic heavy quarks in the Columbia formulation

10.22323/1.164.0126 ◽

2012 ◽

Cited By ~ 2

Author(s):

Christoph Lehner

Keyword(s):

Perturbation Theory ◽

Heavy Quarks ◽

Lattice Perturbation Theory ◽

Lattice Perturbation

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Tuning improved anisotropic actions in lattice perturbation theory

10.22323/1.066.0212 ◽

2009 ◽

Author(s):

Justin Foley

Keyword(s):

Perturbation Theory ◽

Lattice Perturbation Theory ◽

Lattice Perturbation

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Supersymmetric Ward-Takahashi identity in one-loop lattice perturbation theory: General procedure

Physical Review D ◽

10.1103/physrevd.70.054504 ◽

2004 ◽

Vol 70 (5) ◽

Cited By ~ 7

Author(s):

Alessandra Feo

Keyword(s):

Perturbation Theory ◽

General Procedure ◽

Lattice Perturbation Theory ◽

Lattice Perturbation

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Perturbative Renormalization of Wilson line operators

EPJ Web of Conferences ◽

10.1051/epjconf/201817506025 ◽

2018 ◽

Vol 175 ◽

pp. 06025 ◽

Cited By ~ 1

Author(s):

Martha Constantinou ◽

Haralambos Panagopoulos

Keyword(s):

Perturbation Theory ◽

Wide Class ◽

Lattice Spacing ◽

Wilson Line ◽

Gauge Invariant ◽

Loop Level ◽

Perturbative Renormalization ◽

Lattice Perturbation Theory ◽

Lattice Perturbation

We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such ‘long-link’ operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributions.

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

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-14-00004.1 ◽

2014 ◽

Vol 31 (10) ◽

pp. 2078-2087 ◽

Cited By ~ 6

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.

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