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Register a new userPlanck scale effects on some low energy quantum phenomena
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Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.
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The superfluid transition in liquid 4He filled in Gelsil glass observed in recent experiments is discussed in the framework of quantum critical phenomena. We show that quantum fluctuations of phase are indeed important at the experimentally studied temperature range owing to the small pore size of Gelsil, in contrast to 4He filled in previously studied porous media such as Vycor glass. As a consequence of an effective particle-hole symmetry, the quantum critical phenomena of the system are described by the 4D XY universality class, except at very low temperatures. The simple scaling agrees with the experimental data remarkably well.
The hypothesis that non-perturbative gravitational effects lead to explicit breaking of global symmetries is considered in the context of Majoron models. We find that the nonvanishing Majoron mass generated by these effects can overclose the universe unless the massive Majoron is unstable. The cosmological mass density constraints can then be satisfied only if $V_{BL} < 10$ TeV, where $V_{BL}$ is the scale of $B-L$ symmetry breaking.
The parity-preserving $U_A(1)times U_a(1)$ massive QED$_3$ is ultraviolet finiteness -- exhibits vanishing $beta$-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern-Simons mass parameter, and all the anomalous dimensions of the fields -- as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme.
Quantum embedding theories provide a feasible route for obtaining quantitative descriptions of correlated materials. However, a critical challenge is solving an effective impurity model of correlated orbitals embedded in an electron bath. Many advanced impurity solvers require the approximation of a bath continuum using a finite number of bath levels, producing a highly nonconvex, ill-conditioned inverse problem. To address this drawback, this study proposes an efficient fitting algorithm for matrix-valued hybridization functions based on a data-science approach, sparse modeling, and a compact representation of Matsubara Greens functions. The efficiency of the proposed method is demonstrated by fitting random hybridization functions with large off-diagonal elements as well as those of a 20-orbital impurity model for a high-Tc compound, LaAsFeO, at low temperatures (T). The results set quantitative goals for the future development of impurity solvers toward quantum embedding simulations of complex correlated materials.
The Casimir force between parallel lines in a theory describing condensed vortices in a plane is determined. We make use of the relation between a Chern-Simons-Higgs model and its dualized version, which is expressed in terms of a dual gauge field and a vortex field. The dual model can have a phase of condensed vortices and, in this phase, there is a mapping to a model of two non-interacting massive scalar fields from which the Casimir force can readily be obtained. The choice of boundary conditions required for the mapped scalar fields and their association with those for the vectorial field and the issues involved are discussed. We also briefly discuss the implications of our results for experiments related to the Casimir effect when vortices can be present.
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