Abstract We prove sharp universal upper bounds on the number of linearly independent steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We ...show that the bounds depend only on the dimension of the system and not on the details of the dynamics. A comparison with similar bounds deriving from a recent spectral conjecture for Markovian evolutions is also provided.
The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, ...uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.
Quantum chaotic interacting N-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales ∼logN. Here, we show that, near criticality, ...certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-N limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing ℏ/τ, again given by τ∼logN. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasiperiodic recurrences indicating reversibility.
We discuss an isomorphism between the possible anomalies of (d + 1)-dimensional quantum field theories with Z2 unitary global symmetry, and those of d-dimensional quantum field theories with ...time-reversal symmetry T. This correspondence is an instance of symmetry defect decoration. The worldvolume of a Z2 symmetry defect is naturally invariant under T , and bulk Z2 anomalies descend to T anomalies on these defects. We illustrate this correspondence in detail for (1 + 1) d bosonic systems where the bulk Z2 anomaly leads to a Kramers degeneracy in the symmetry defect Hilbert space and exhibits examples. We also discuss (1 + 1) d fermion systems protected by Z2 global symmetry where interactions lead to a Z 8 classification of anomalies. Under the correspondence, this is directly related to the Z8 classification of (0 + 1) d fermions protected by T. Finally, we consider (3 + 1) d bosonic systems with Z2 symmetry where the possible anomalies are classified by Z2 × Z2. We construct topological field theories realizing these anomalies and show that their associated symmetry defects support anyons that can be either fermions or Kramers doublets.
We use self-consistent Hartree-Fock calculations performed in the full π-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer ...graphene (TBG). We find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected C_{2}T symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling n=±p/4 with integer p=1, 2, 3, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ∼20, the gapped states do not necessarily break C_{2}T symmetry and as a consequence the insulating states at n=±1/4 and n=±3/4 need not exhibit a quantized anomalous Hall effect.
In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution ...methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their
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-cut representation form in the Hilbert space
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. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.
Although genuine multipartite entanglement has already been generated and verified by experiments, most of the existing measures cannot detect genuine entanglement faithfully. In this work, by ...exploiting for the first time a previously overlooked constraint for the distribution of entanglement in three-qubit systems, we reveal a new genuine tripartite entanglement measure, which is related to the area of a so-called concurrence triangle. It is compared with other existing measures and is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space. The properties of the triangle measure make it a candidate in potential quantum tasks and available to be used in any multiparty entanglement problems.
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