19,127 research outputs found
Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities
In the first part of the paper we survey some nonlocal flows of convex plane
curves ever studied so far and discuss properties of the flows related to
enclosed area and length, especially the isoperimetric ratio and the
isoperimetric difference. We also study a new nonlocal flow of convex plane
curves and discuss its evolution behavior. In the second part of the paper we
discuss necessary and sufficient conditions (in terms of the (mixed)
isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed
curves to be homothetic or parallel.Comment: 23 page
Suppression of long-wavelength CMB spectrum from the no-boundary initial condition
The lack of correlations at the long-wavelength scales of the cosmic
microwave background spectrum is a long-standing puzzle and it persists in the
latest Planck data. By considering the Hartle-Hawking no-boundary wave function
as the initial condition of the inflationary universe, we propose that the
power suppression can be the consequence of a massive inflaton, whose initial
vacuum is the Euclidean instanton in a compact manifold. We calculate the
primordial power spectrum of the perturbations, and find that as long as the
scalar field is moderately massive, the power spectrum is suppressed at the
long-wavelength scales.Comment: 9 pages, 7 figures; journal versio
Robust ground-state energy estimation under depolarizing noise
We present a novel ground-state energy estimation algorithm that is robust
under global depolarizing error channels. Building upon the recently developed
Quantum Exponential Least Squares (QCELS) algorithm [Ding, Lin, PRX Quantum, 4,
020331, 2023], our new approach incorporates significant advancements to ensure
robust estimation while maintaining a polynomial cost in precision. By
leveraging the spectral gap of the Hamiltonian effectively, our algorithm
overcomes limitations observed in previous methods like quantum phase
estimation (QPE) and robust phase estimation (RPE). Going beyond global
depolarizing error channels, our work underscores the significance and
practical advantages of utilizing randomized compiling techniques to tailor
quantum noise towards depolarizing error channels. Our research demonstrates
the feasibility of ground-state energy estimation in the presence of
depolarizing noise, offering potential advancements in error correction and
algorithmic-level error mitigation for quantum algorithms.Comment: 35 pages, 8 figures. The first two authors contributed equally to
this wor
Effective conductivity of composites of graded spherical particles
We have employed the first-principles approach to compute the effective
response of composites of graded spherical particles of arbitrary conductivity
profiles. We solve the boundary-value problem for the polarizability of the
graded particles and obtain the dipole moment as well as the multipole moments.
We provide a rigorous proof of an {\em ad hoc} approximate method based on the
differential effective multipole moment approximation (DEMMA) in which the
differential effective dipole approximation (DEDA) is a special case. The
method will be applied to an exactly solvable graded profile. We show that DEDA
and DEMMA are indeed exact for graded spherical particles.Comment: submitted for publication
Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram
The discrete time path integral Monte Carlo (PIMC) with a one-particle
density matrix approximation is applied to study the quantum phase transition
in the coupled double-well chain. To improve the convergence properties, the
exact action for a single particle in a double well potential is used to
construct the many-particle action. The algorithm is applied to the interacting
quantum double-well chain for which the zero-temperature phase diagram is
determined. The quantum phase transition is studied via finite-size scaling and
the critical exponents are shown to be compatible with the classical
two-dimensional (2D) Ising universality class -- not only in the order-disorder
limit (deep potential wells) but also in the displacive regime (shallow
potential wells).Comment: 17 pages, 7 figures; Accepted for publication in Phys. Rev.
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