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Justin H. Wilson

Bio: Justin H. Wilson is an academic researcher from Rutgers University. The author has contributed to research in topics: Casimir effect & Vacuum energy. The author has an hindex of 16, co-authored 44 publications receiving 825 citations. Previous affiliations of Justin H. Wilson include Texas A&M University & University of Maryland, College Park.

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TL;DR: In this article, the authors numerically study the phase transition of Haar-random quantum circuits in 1 + 1 dimensions and extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates.
Abstract: We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate ${p}_{c}=0.17(1)$. We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from those for stabilizer circuits or percolation, but we cannot definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies ${S}_{n}$ depends strongly on the R\'enyi index $n$; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.

164 citations

Journal ArticleDOI
TL;DR: It is unveiled how out-of-equilibrium states, prepared via a quantum quench in a two-band system, can exhibit a nonzero Hall-type current-a remnant Hall response-even when the instantaneous Hamiltonian is time reversal symmetric (in contrast to equilibrium Hall currents).
Abstract: Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here, we unveil how out-of-equilibrium states, prepared via a quantum quench in a two-band system, can exhibit a nonzero Hall-type current—a remnant Hall response—even when the instantaneous Hamiltonian is time reversal symmetric (in contrast to equilibrium Hall currents). Interestingly, the remnant Hall response arises from the coherent dynamics of the wave function that retain a remnant of its quantum geometry postquench, and can be traced to processes beyond linear response. Quenches in two-band Dirac systems are natural venues for realizing remnant Hall currents, which exist when either mirror or time-reversal symmetry are broken (before or after the quench). Its long time persistence, sensitivity to symmetry breaking, and decoherence-type relaxation processes allow it to be used as a sensitive diagnostic of the complex out-of-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.

77 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the case of quantum graphs, a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices.
Abstract: In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a 'Laplacian') with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e. conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H = A*A, and relating the constant term to the index of A. An independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions. It is also found that the algebraic multiplicity of 0 as a root of the secular determinant of H is the sum of the nullities of A and A*.

69 citations

Journal ArticleDOI
12 Jun 2020
TL;DR: In this article, a theory for twisted bilayer graphene with a random twist angle using a lattice model was presented, which allows the twist angle to appear as a free parameter and characterized the effects of twist angle disorder on the formation of a moir\'e superlattice miniband, the Dirac cone velocity, and the van Hove singularities in the density of states.
Abstract: This work presents a theory for twisted bilayer graphene with a random twist angle using a lattice model of twisted bilayer graphene that allows the twist angle to appear as a free parameter. The authors characterize the effects of twist-angle disorder on the formation of a moir\'e superlattice miniband, the Dirac cone velocity, and the van Hove singularities in the density of states.

65 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that for the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat kernel expansion is proportional to the trace of the internal scattering matrix of the graph.
Abstract: In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions. It is found also that the algebraic multiplicity of 0 as a root of the secular determinant of H is the sum of the nullities of A and A*.

63 citations


Cited by
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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

01 Feb 2012
TL;DR: In this article, the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials, and particular space groups also allow 3D Dirac points as symmetry protected degeneracies.
Abstract: We show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO(2) which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO(2) is metastable, so it can be physically realized as a 3D analog to graphene.

763 citations

Journal ArticleDOI
TL;DR: Chisholm and Morris as discussed by the authors presented a collection of mathematical texts written expressly for the physicist, with a focus on the needs of modern undergraduate physics students, and they suggested that the book might also be useful to undergraduates in chemistry and engineering and research workers in other fields.
Abstract: Volume II J. S. R. Chisholm and Rosa M. Morris Amsterdam: North-Holland. 1964 Pp. xviii + 717. Price 72s. This book is a valuable addition to an ever-growing collection of mathematical texts written expressly for the physicist. The authors suggest that the book might also be useful to undergraduates in chemistry and engineering and research workers in other fields, but the content is clearly chosen to meet the needs of modern undergraduate physics.

474 citations