Renormalization-group results of electronic states in a one-dimensional system with incommensurate potentials

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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Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

Scientific Reports ◽

10.1038/s41598-021-92390-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Milad Jangjan ◽

Mir Vahid Hosseini

Keyword(s):

Phase Transition ◽

Dimensional System ◽

Inversion Symmetry ◽

Topological Phase ◽

Edge States ◽

Zero Energy ◽

One Dimensional ◽

Topological Phase Transition ◽

Metal State ◽

Topological Metal

AbstractWe theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

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AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

Journal of High Energy Physics ◽

10.1007/jhep04(2021)110 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Yolanda Lozano ◽

Carlos Nunez ◽

Anayeli Ramirez

Keyword(s):

Quantum Mechanics ◽

Riemann Surface ◽

Central Charge ◽

Global Solutions ◽

Infinite Family ◽

Dimensional System ◽

One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

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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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