23,104 research outputs found
Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces
Let be the smooth boundary of a bounded strongly pseudo-convex
domain in a complete Stein manifold . Then (1) For ,
admits a pseudo-Eistein metric; (2) For , admits
a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly
pseudoconvex CR embeddable 3-manifold , its CR Paneitz operator is a
closed operator
A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
We extend a standard stochastic theory to study open quantum systems coupled
to generic quantum environments including the three fundamental classes of
noninteracting particles: bosons, fermions and spins. In this unified
stochastic approach, the generalized stochastic Liouville equation (SLE)
formally captures the exact quantum dissipations when noise variables with
appropriate statistics for different bath models are applied. Anharmonic
effects of a non-Gaussian bath are precisely encoded in the bath multi-time
correlation functions that noise variables have to satisfy. Staring from the
SLE, we devise a family of generalized hierarchical equations by averaging out
the noise variables and expand bath multi-time correlation functions in a
complete basis of orthonormal functions. The general hiearchical equations
constitute systems of linear equations that provide numerically exact
simulations of quantum dynamics. For bosonic bath models, our general
hierarchical equation of motion reduces exactly to an extended version of
hierarchical equation of motion which allows efficient simulation for arbitrary
spectral densities and temperature regimes. Similar efficiency and exibility
can be achieved for the fermionic bath models within our formalism. The spin
bath models can be simulated with two complementary approaches in the presetn
formalism. (I) They can be viewed as an example of non-Gaussian bath models and
be directly handled with the general hierarchical equation approach given their
multi-time correlation functions. (II) Alterantively, each bath spin can be
first mapped onto a pair of fermions and be treated as fermionic environments
within the present formalism.Comment: 31 pages, 2 figure
Probing medium-induced jet splitting and energy loss in heavy-ion collisions
The nuclear modification of jet splitting in relativistic heavy-ion
collisions at RHIC and the LHC energies is studied based on the higher twist
formalism. Assuming coherent energy loss for the two splitted subjets, a
non-monotonic jet energy dependence is found for the nuclear modification of
jet splitting function: strongest modification at intermediate jet energies
whereas weaker modification for larger or smaller jet energies. Combined with
the smaller size and lower density of the QGP medium at RHIC than at the LHC,
this explains the CMS-STAR groomed jet puzzle -- strong nuclear modification of
the momentum sharing distribution at the LHC whereas no obvious
modification of the distribution at RHIC. In contrast, the observed
nuclear modification pattern of the groomed jet distribution cannot be
explained solely by independent energy loss of the two subjets. Our result may
be tested in future measurements of groomed jets with lower jet energies at the
LHC and larger jet energies at RHIC, for different angular separations between
the two subjets.Comment: 10 pages, 12 figure
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