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At least 235 records · Page 13

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Effect of Prosumer Duality on Power Market: The Effect of Market Regulation

Electricity prosumers are energy subsystems that not only consume, but also produce electricity. They are present in distribution level networks as traditional utility customers who have installed distributed energy resources. They are also present in transmission level networks as large conglomerates own both generation assets and large industrial loads. Previous work on the economics of prosumers has demonstrated that prosumers in a market have incentives to behave more competitively compared to producers and consumers in traditional markets. This paper further explores the behavior of prosumers and their response to market policies including the allocation of network losses and the impact of net metering. We extend a Cournot model of a dual prosumer and find that prosumers respond with higher supply quantities if network losses are allocated to demand base. They respond with lower supply quantities if network losses are allocated to supply base. Allocating network losses to demand base also causes equilibrium prices to decline. Markets where prosumers first satisfy their own load and then sell the balance of electricity to the grid have lower quantities and higher prices compared to markets where prosumers buy and sell at locational marginal price.

Tsybina, Eve↗

Feynman—Schwinger duality

Concise retrospectives of two giants of physics, their origins, similarities, and differences.

99 GENERAL AND MISCELLANEOUS↗

Electron-mirror duality and thermality

Classical electromagnetic radiation from moving point charges is foundational, but the thermal dynamics responsible for classical acceleration temperature are poorly understood. We investigate the thermal properties of classical electromagnetic radiation in the context of the correspondence between accelerated electrons and moving mirrors, focusing on three trajectories with asymptotically infinite (Davies–Fulling), asymptotically zero (Walker–Davies), and eternally uniform acceleration. The latter two are argued not to be thermal, while the former is found to emit thermal photons with a temperature that depends on the electron’s speed. Thermal radiation occurs in the absence of jerk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T . The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1 ± 1 depending on the magnetic charge. We study in detail U(1) U ( 1 ) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4 , e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 2 2 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N) S O ( N ) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

Cordova, Clay↗

Topics in the AdS/CFT Correspondence: Precision tests with Wilson loops, quantum black holes and dualities

The Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence conjectures a mathematical equivalence between string theories and gauge theories. This correspondence and its generalizations allow to address difficult problems of strongly coupled field theory dynamics using weakly couple gravity. It also allows to tackle fundamental questions of gravity, such as black hole entropy, using field theories. The research supported by this grant focused on quantum aspects of the AdS/CFT correspondence at sub-leading level. Various results were obtained for expectation values of supersymmetric Wilson loops and for sub-leading entropy corrections of certain asymptotically AdS black holes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗