Extended Supersymmetric Structures in Gapped and Superconducting Graphene

In view of the many quantum field theoretical descriptions of graphene in 2 + 1 dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the presence of a domain wall and also for superconducting graphene in the presence of a vortex. As we explicitly demonstrate, the gapped graphene electrons that are localized on the domain wall are associated with four N = 2 one-dimensional supersymmetries, with each pair combining to form an extended N = 4 supersymmetry with non-trivial topological charges. The case of superconducting graphene is more involved, with the electrons localized on the vortex being associated with n one-dimensional supersymmetries, which in turn combine to form an N = 2n extended supersymmetry with non-trivial topological charges. As we shall prove, all supersymmetries are unbroken, a feature closely related to the number of the localized fermions and also to the exact form of the associated operators. In addition, the corresponding Witten index is invariant under compact and odd perturbations.

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Fermions in a Reissner–Nordström–anti-de Sitter black hole background and N = 4 supersymmetry with nontrivial topological charges

Modern Physics Letters A ◽

10.1142/s0217732314501314 ◽

2014 ◽

Vol 29 (25) ◽

pp. 1450131 ◽

Cited By ~ 1

Author(s):

V. K. Oikonomou

Keyword(s):

Black Hole ◽

Extended Supersymmetry ◽

Chiral Limit ◽

Central Charge ◽

De Sitter ◽

One Dimensional ◽

Black Hole Background ◽

Witten Index ◽

Topological Charges

We demonstrate that the fermions in Reissner–Nordström–anti-de Sitter black hole background in the chiral limit m = 0, are related to an N = 4 extended one-dimensional supersymmetry with nontrivial topological charges. We also show that the N = 4 extended supersymmetry is unbroken and we extend the two N = 2 one-dimensional supersymmetries that the system also possesses, to have a trivial central charge. The implications of the trivial central charge on the Witten index are also discussed.

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Chiral Topological Phases and Fractional Domain Wall Excitations in One-Dimensional Chains and Wires

Physical Review Letters ◽

10.1103/physrevlett.107.166804 ◽

2011 ◽

Vol 107 (16) ◽

Cited By ~ 19

Author(s):

Jukka I. Väyrynen ◽

Teemu Ojanen

Keyword(s):

Domain Wall ◽

Topological Phases ◽

One Dimensional

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EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

International Journal of Modern Physics B ◽

10.1142/s0217979296001847 ◽

1996 ◽

Vol 10 (25) ◽

pp. 3451-3459 ◽

Cited By ~ 2

Author(s):

ANTÓNIO M.R. CADILHE ◽

VLADIMIR PRIVMAN

Keyword(s):

Exact Solution ◽

Domain Wall ◽

Nearest Neighbor ◽

Spin Exchange ◽

Initial Conditions ◽

Strong Dependence ◽

Zero Temperature ◽

Dimensional Model ◽

One Dimensional ◽

Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

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Conclusion: Detroit and the future of the city

Why Detroit Matters ◽

10.1332/policypress/9781447327868.003.0028 ◽

2017 ◽

Author(s):

Brian Doucet

Keyword(s):

Power Relations ◽

Critical Assessment ◽

One Dimensional ◽

Marginal Groups ◽

The Future ◽

The Many ◽

The City

In this concluding chapter, the main strands of through within the book are brought together. The main narrative of Detroit as a symbol of urban failure is briefly discussed before shifting to a critical assessment of the city’s emerging narrative: that of comeback and renaissance. Both these one-dimensional narratives are treated as problematic and critiqued by using relevant chapters from the book. Two main policy and political insights are highlighted. The first is that much of Detroit’s decline has been a factor produced outside its boundaries so its solutions need to be thought of at these geographic scales. The second relates to working towards including different voices and perspectives about the future of the city and rethinking how power relations can give marginal groups real input into the systems which shape their lives. The many interviews and perspectives in this book provide pathways towards inclusive, fair and just cities.

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ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887806001697 ◽

2006 ◽

Vol 03 (07) ◽

pp. 1303-1312 ◽

Cited By ~ 1

Author(s):

WEIGANG QIU ◽

FEI SUN ◽

HONGBAO ZHANG

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Theory ◽

Casimir Effect ◽

Minkowski Spacetime ◽

Quantum Field ◽

Explicit Result ◽

Massless Spin ◽

The Many ◽

The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

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p-Adic Path Integrals for Quadratic Actions

Modern Physics Letters A ◽

10.1142/s0217732397001485 ◽

1997 ◽

Vol 12 (20) ◽

pp. 1455-1463 ◽

Cited By ~ 21

Author(s):

G. S. Djordjević ◽

B. Dragovich

Keyword(s):

Quantum Mechanics ◽

Path Integral ◽

Path Integrals ◽

Probability Amplitude ◽

Exact Form ◽

Feynman Path Integral ◽

Feynman Path ◽

One Dimensional ◽

Ordinary Quantum

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude [Formula: see text] for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

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Quantum Many-Particle Systems and Second Quantization

Models of Quantum Matter ◽

10.1093/oso/9780199678839.003.0002 ◽

2019 ◽

pp. 5-44

Author(s):

Hans-Peter Eckle

Keyword(s):

Quantum Mechanics ◽

Particle Physics ◽

Mathematical Formulation ◽

Particle Systems ◽

Quantum Field ◽

Second Quantization ◽

Creation And Annihilation Operators ◽

Quantum Matter ◽

Interacting Systems ◽

The Many

Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.

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Energy levels of one-dimensional anharmonic oscillator via neural networks

Modern Physics Letters A ◽

10.1142/s0217732319500883 ◽

2019 ◽

Vol 34 (12) ◽

pp. 1950088 ◽

Cited By ~ 1

Author(s):

Halil Mutuk

Keyword(s):

Neural Network ◽

Field Theory ◽

Anharmonic Oscillator ◽

Energy Levels ◽

High Accuracy ◽

Network System ◽

Quantum Field ◽

One Dimensional ◽

Neural Network System ◽

Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

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