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arXiv2018

Spin networks on adiabatic quantum computer

The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

gr-qc↗

arXiv2022

Lie Symmetries, Painlevé analysis and global dynamics for the temporal equation of radiating stars

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of asymptotic solutions. Moreover, with the application of Lie's theory, we can reduce the order of the master differential equation, while an exact similarity solution is determined. Finally, the master equation possesses the Painlevé property, which means that the analytic solution can be expressed in terms of a Laurent expansion.

gr-qc↗

arXiv2018

Positive gravitational subsystem energies from CFT cone relative entropies

The positivity of relative entropy for spatial subsystems in a holographic CFT implies the positivity of certain quantities in the dual gravitational theory. In this note, we consider CFT subsystems whose boundaries lie on the lightcone of a point $p$. We show that the positive gravitational quantity which corresponds to the relative entropy for such a subsystem $A$ is a novel notion of energy associated with a gravitational subsystem bounded by the minimal area extremal surface $\tilde{A}$ associated with $A$ and by the AdS boundary region $\hat{A}$ corresponding to the part of the lightcone from $p$ bounded by $\partial A$. This generalizes the results of arXiv:1605.01075 for ball-shaped regions by making use of the recent results in arXiv:1703.10656 for the vacuum modular Hamiltonian of regions bounded on lightcones. As part of our analysis, we give an analytic expression for the extremal surface in pure AdS associated with any such region $A$. We note that its form immediately implies the Markov property of the CFT vacuum (saturation of strong subadditivity) for regions bounded on the same lightcone. This gives a holographic proof of the result proven for general CFTs in arXiv:1703.10656. A similar holographic proof shows the Markov property for regions bounded on a lightsheet for non-conformal holographic theories defined by relevant perturbations of a CFT.

hep-th↗

arXiv2018

Extended Riemannian Geometry I: Local Double Field Theory

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2- and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covariant form of the strong section condition. Furthermore, it should provide a useful step towards global and coordinate invariant descriptions of T- and U-duality invariant field theories.

hep-th↗

arXiv2013

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich--Witten tau-function.

hep-th↗

arXiv2018

Vacuum Magnetic Birefringence Experiment as a probe of Dark Sector

Vacuum magnetic birefringence (VMB) is a nonlinear electromagnetic effect predicted by QED. In addition to the effect from QED, the effect also has a possibility to probe the dark sector. The effect predicted by QED is parity conservative, but the effect from the dark sector can induce parity violation. To pursue this possibility, we calculated the effect from the dark sector with the generalized Heisenberg-Euler effective Lagrangian that is applicable to parity-violating theories. Various dark sector models exist, among which the contribution of the dark sector neutrinos to the VMB experiment is examined. The contribution comes from the mixing of photon with the dark sector Z boson and violates parity, thus inducing a parity-violating electromagnetic interaction. If the polarization vector is denoted by $ε(θ_i)$ when its direction is rotated by an angle $θ_i$ from the direction of the applied magnetic field, the change of the polarization from $ε(45^\circ)$ to $ε(-45^\circ)$ and vice versa are examined. The contribution from the dark sector modifies the magnitude of the polarization change, so it can be detected by measuring the magnitude precisely. In addition to the change in the magnitude, the dark sector also induces parity-violating effects. We also propose a new scheme to measure the effect of parity violation directly. By measuring the change of polarization from $ε(0^{\circ})$ to $ε(90^\circ)$, and vice versa, with a ring Fabry-Pérot resonator, one can search for the effect directly. The signal that appears in this scheme is evidence of parity violation from beyond standard model theories.

hep-ph↗

arXiv2011

Repulsive long-range forces between anisotropic atoms and dielectrics

We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the objects is repulsive are constructed. Such configurations exist for three anisotropic atoms as well as for an anisotropic atom above a dielectric plate with a hole whose permittivity is anisotropic. Apart from the absolute magnitude of the force, the dependence on the configuration is qualitatively the same as for metallic objects for which the anisotropy is a purely geometric effect. In the weak limit closed analytic expressions for rather complicated configurations are obtained. The non-monotonic dependence of the interaction energy on separation is related to the fact that the electromagnetic Green's dyadic is not positive definite. The analysis in the weak limit is found to also semi-quantitatively explain the dependence of Casimir forces on the orientation of anisotropic dielectrics observed experimentally. Contrary to the scalar case, irreducible electromagnetic three-body energies can change sign. We trace this to the fact that the electromagnetic Green's dyadic is not positive definite.

physics.atom-ph↗

arXiv2012

WKB Analysis of PT-Symmetric Sturm-Liouville problems. II

In a previous paper it was shown that a one-turning-point WKB approximation gives an accurate picture of the spectrum of certain non-Hermitian PT-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to which this analysis applies include the linear potential $V=igx$ and the sinusoidal potential $V=ig\sin(αx)$. However, the one-turning-point analysis fails to give the full structure of the spectrum for the cubic potential $V=igx^3$, and in particular it fails to reproduce the critical points at which two real eigenvalues merge and become a complex-conjugate pair. The present paper extends the method to cases where the WKB path goes through a {\it pair} of turning points. The extended method gives an extremely accurate approximation to the spectrum of $V=igx^3$, and more generally it works for potentials of the form $V=igx^{2N+1}$. When applied to potentials with half-integral powers of $x$, the method again works well for one sign of the coupling, namely that for which the turning points lie on the first sheet in the lower-half plane.

hep-th↗

arXiv2012

Quantum Bose and Fermi gases with large negative scattering length in the 2-body S-matrix approximation

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many body processes that are reducible to 2-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons, and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a meta-stable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.

cond-mat.quant-gas↗

arXiv2010

Correlated Topological Insulators and the Fractional Magnetoelectric Effect

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically non-trivial spaces. We illustrate this result with a concrete example of a time reversal symmetric topological insulator of correlated bosons with theta = pi/4. Extensions to electronic fractional topological insulators are briefly described.

cond-mat.str-el↗

arXiv2011

Effective Field Theory of Fractional Quantized Hall Nematics

We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory -- which is shown to be its dual -- on a more microscopic basis and enables us to compute a ground state wave function in the symmetry-broken phase. In such a state of matter, the Hall resistance remains quantized while the longitudinal DC resistivity due to thermally-excited quasiparticles is anisotropic. We interpret recent experiments at Landau level filling factor ν=7/3 in terms of our theory.

cond-mat.str-el↗

arXiv2012

Real-space entanglement spectrum of quantum Hall systems

We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely-related particle entanglement spectrum, and carry out the Schmidt decomposition of the Laughlin state analytically at large size.

cond-mat.mes-hall↗

arXiv2012

Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity

We derive from first principles the Kubo formulas for the stress-stress response function at zero wavevector that can be used to define the full complex frequency-dependent viscosity tensor, both with and without a uniform magnetic field. The formulas in the existing literature are frequently incomplete, incorrect, or lack a derivation; in particular, Hall viscosity is overlooked. Our approach begins from the response to a uniform external strain field, which is an active time-dependent coordinate transformation in d space dimensions. These transformations form the group GL(d,R) of invertible matrices, and the infinitesimal generators are called strain generators. These enable us to express the Kubo formula in different ways, related by Ward identities; some of these make contact with the adiabatic transport approach. For Galilean-invariant systems, we derive a relation between the stress response tensor and the conductivity tensor that is valid at all frequencies and in both the presence and absence of a magnetic field. In the presence of a magnetic field and at low frequency, this yields a relation between the Hall viscosity, the q^2 part of the Hall conductivity, the inverse compressibility (suitably defined), and the diverging part of the shear viscosity (if any); this relation generalizes a result found recently. We show that the correct value of the Hall viscosity at zero frequency can be obtained (at least in the absence of low-frequency bulk and shear viscosity) by assuming that there is an orbital spin per particle that couples to a perturbing electromagnetic field as a magnetization per particle. We study several examples as checks on our formulation.

cond-mat.stat-mech↗

arXiv2011

The existence of a two-solar mass neutron star constrains the gravitational constant G_N at strong field

In General Relativity there is a maximum mass allowed for neutron stars that, if exceeded, entails their collapse into a black hole. Its precise value depends on details of the nuclear matter equation of state about which we are much more certain thanks to recent progress in low-energy effective theories. The discovery of a two-solar mass neutron star, near that maximum mass, when analyzed with modern equations of state, implies that Newton's gravitational constant in the star cannot exceed its value on Earth by more than 8% at 95% confidence level. This is a remarkable leap of ten orders of magnitude in the gravitational field intensity at which the constant has been constrained.

gr-qc↗

arXiv2013

Nucleon-Meson Couplings in One Boson Exchange Potential using Non-Critical String Theory

A non-critical holographic QCD model constructed in the six dimensional Anti-de-Sitter ($AdS_6$) supergravity background is employed to study a the baryon. It is shown that the size of the baryon is of order one with respect to the $λ$, however, it is smaller than the scale of the dual QCD. An effective four dimensional action for the nucleon is obtained in terms of the meson exchange potentials. All meson-nucleon couplings in the non-critical $AdS_6$ background are calculated. Results obtained using our model are compared with predictions of four modern phenomenological interaction models. Also, our numerical results are compared with the results of the Sakai-Sugimoto (SS) model which indicate that the non-critical holographic QCD model can be a good toy to calculate the meson-nucleon couplings.

hep-th↗

arXiv2011

Superspace Parafermions

We describe several families of non-unitary coset conformal field theories that possess truly marginal couplings. These generalize the known examples of Wess-Zumino-Witten models on supergroups such as PSU(n|n) or OSP(2n+2|2n). Our extension includes coset space sigma models, affine Toda theories or Gross-Neveu models which are believed to arise in certain limits.

hep-th↗

arXiv2011

Cosmological observables, IR growth of fluctuations, and scale-dependent anisotropies

We extend semiclassical methods in inflationary cosmology that capture leading IR corrections to correlators. Such large IR effects can be absorbed into a coordinate change when examining sufficiently local observables, but not when comparing observations at large separation in scales, such as seen by a late-time observer. The analysis is facilitated by definition of a scale-dependent metric and physical momentum. These assist definition of "IR-safe" observables seen by a post-inflationary observer, which are contrasted to those based on the local geometry of the reheating surface. For such observables, the observer's horizon provides an effective IR cutoff. IR growth contributes to enhanced statistical inhomogeneities/anisotropies at short scales, observation of which by a present day observer might be sought in 21 cm measurements. Such IR corrections are argued to grow large for a very late-time observer.

hep-th↗

arXiv2011

Randall-Sundrum limit of f(R) brane-world models

By setting some special boundary conditions in the variational principle we obtain junction conditions for the five-dimensional $f(R)$ gravity which in the Einstein limit $f(R)\rightarrow R$ transform into the standard Randall-Sundrum junction conditions. We apply these junction conditions to a particular model of a Friedmann universe on the brane and show explicitly that the limit gives the standard Randall-Sundrum model Friedmann equation.

hep-th↗