Time-dependent Mass Term Research Articles

Flat band assisted topological charge pump in the dice lattice

We comparatively study the possible topological charge pump (TCP) in the Dice lattice by considering two types of time-dependent mass terms of the Dirac electrons, the ${S}_{z}$ and $U$ term, which are taken as the pumping potentials. It is shown that the former ${S}_{z}$ pumping potential preserving the electron-hole symmetry of the system leads to a vanishing charge pump, whereas the later $U$ mass term breaking the electron-hole symmetry can pump out an integer number of charges in a pumping cycle, even the Berry phases of Dirac electrons in both cases are the same vanishing, $\ensuremath{\gamma}=0$. The topological interface state (TIS), due to the flat bands bridging the two pumping regions not from the Dirac-cone bands, can account for the TCP found in the $U$-mass pumping case and oppositely, there is no TIS due to the flat bands in the ${S}_{z}$ pumping case. Our findings imply that the flat band in the Dice lattice may contribute to the electron transport under appropriate settings.

Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass

<p style='text-indent:20px;'>In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and blow-up results are obtained to both sub-critical and critical cases with corresponding upper bound lifespan estimates. For the sub-critical case, our argument does not rely on the sign condition of dissipation and mass, which gives the extension of the result in [<xref ref-type="bibr" rid="b14">14</xref>]. Moreover, we show the blow-up result for the critical case which is a new result.</p>

Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.

Quasimatter bounce equivalent to Starobinsky inflation

In this paper we construct a bounce model that mimics the Starobinsky inflationary model. Our construction relies on Wands' duality, which shows that the Mukhanov-Sasaki equation has a symmetry transformation by changing appropriately its time-dependent mass term. One of the advantages of this constructive method is that one can control every contribution to the primordial power spectrum and check how far we can emulate a given primordial model with a different scenario. In particular, we show that mapping the Starobinsky inflation into a quasi-matter bounce gives the correct relation between the scalar spectral index $n_s-1$ and the tensor-to-scalar ratio $r$.

A scale of critical exponents for semilinear waves with time-dependent damping and mass terms

We consider the following Cauchy problem for a wave equation with time-dependent damping term b(t)ut and mass term m(t)2u, and a power nonlinearity |u|p: utt−Δu+b(t)ut+m2(t)u=|u|p,t≥0,x∈Rn,u(0,x)=f(x),ut(0,x)=g(x).We discuss how the interplay between an effective time-dependent damping term and a time-dependent mass term influences the decay rate of the solution to the corresponding linear Cauchy problem, in the case in which the mass is dominated by the damping term, i.e. m(t)=o(b(t)) as t→∞.Then we use the obtained estimates of solutions to linear Cauchy problems to prove the existence of global in-time energy solutions to the Cauchy problem with power nonlinearity |u|p at the right-hand side of the equation, in a supercritical range p>p̄, assuming small data in the energy space (f,g)∈H1×L2. In particular, we find a threshold case for the behavior of m(t) with respect to b(t).Below the threshold, the mass has no influence on the critical exponent, so that p̄=1+4∕n, as in the case with m=0. Above the threshold, p̄=1, global (in time) small data energy solutions exist for any p>1, as it happens for the classical damped Klein–Gordon equation (b=m=1). Along the threshold, varying a parameter β∈[0,∞] which depends on the behavior of m(t) with respect to b(t), we find a scale of critical exponents, namely, p̄=1+4∕(n+4β).This scale of critical exponents is consistent with the diffusion phenomenon, that is, it is the same scale of critical exponents of the Cauchy problem for the corresponding diffusive equation −Δv+b(t)vt+m2(t)v=|v|p,t≥0,x∈Rn,v(0,x)=φ(x).

Non-Hermitian interaction representation and its use in relativistic quantum mechanics

The textbook interaction-picture formulation of quantum mechanics is extended to cover the unitarily evolving systems in which the Hermiticity of the observables is guaranteed via an ad hoc amendment of the inner product in Hilbert space. These systems are sampled by the Klein–Gordon equation with a space- and time-dependent mass term.

Time-dependent stabilization in AdS/CFT

We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons.

Inflation from charged scalar and primordial magnetic fields?

A model of inflation is presented where the inflaton field is a complex scalar field coupled to a U(1) gauge field. Due to the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by U(1). Due to the coupling of the inflaton to the gauge field, a time dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent U(1) gauge kinetic coupling.

Multiple M2-branes and plane waves

We propose a natural generalisation of the BLG multiple M2-brane action to membranes in curved plane wave backgrounds, and verify in two different ways that the action correctly captures the non-trivial space-time geometry. We show that the M2 to D2 reduction of the theory along a non-trivial direction in field space is equivalent to the D2-brane world-volume Yang-Mills theory with a non-trivial (null-time dependent) dilaton in the corresponding IIA background geometry. As another consistency check of this proposal we show that the properties of metric 3-algebras ensure the equivalence of the Rosen coordinate version of this action (time-dependent metric on the space of 3-algebra valued scalar fields, no mass terms) and its Brinkmann counterpart (constant couplings but time-dependent mass terms). We also establish an analogous result for deformed Yang-Mills theories in any dimension which, in particular, demonstrates the equivalence of the Rosen and Brinkmann forms of the plane wave matrix string action.