18,275 research outputs found
Gauge invariant hydrogen atom Hamiltonian
For quantum mechanics of a charged particle in a classical external
electromagnetic field, there is an apparent puzzle that the matrix element of
the canonical momentum and Hamiltonian operators is gauge dependent. A
resolution to this puzzle is recently provided by us in [2]. Based on the
separation of the electromagnetic potential into pure gauge and gauge invariant
parts, we have proposed a new set of momentum and Hamiltonian operators which
satisfy both the requirement of gauge invariance and the relevant commutation
relations. In this paper we report a check for the case of the hydrogen atom
problem: Starting from the Hamiltonian of the coupled electron, proton and
electromagnetic field, under the infinite proton mass approximation, we derive
the gauge invariant hydrogen atom Hamiltonian and verify explicitly that this
Hamiltonian is different from the Dirac Hamiltonian, which is the time
translation generator of the system. The gauge invariant Hamiltonian is the
energy operator, whose eigenvalue is the energy of the hydrogen atom. It is
generally time-dependent. In this case, one can solve the energy eigenvalue
equation at any specific instant of time. It is shown that the energy
eigenvalues are gauge independent, and by suitably choosing the phase factor of
the time-dependent eigenfunction, one can ensure that the time-dependent
eigenfunction satisfies the Dirac equation.Comment: 7 pages, revtex4, some further discussion on Dirac Hamiltonian and
the gauge invariant Hamiltonian is added, one reference removed; new address
of some of the authors added, final version to appear in Phys. Rev.
Beyond Prediction: On-street Parking Recommendation using Heterogeneous Graph-based List-wise Ranking
To provide real-time parking information, existing studies focus on
predicting parking availability, which seems an indirect approach to saving
drivers' cruising time. In this paper, we first time propose an on-street
parking recommendation (OPR) task to directly recommend a parking space for a
driver. To this end, a learn-to-rank (LTR) based OPR model called OPR-LTR is
built. Specifically, parking recommendation is closely related to the "turnover
events" (state switching between occupied and vacant) of each parking space,
and hence we design a highly efficient heterogeneous graph called ESGraph to
represent historical and real-time meters' turnover events as well as
geographical relations; afterward, a convolution-based event-then-graph network
is used to aggregate and update representations of the heterogeneous graph. A
ranking model is further utilized to learn a score function that helps
recommend a list of ranked parking spots for a specific on-street parking
query. The method is verified using the on-street parking meter data in Hong
Kong and San Francisco. By comparing with the other two types of methods:
prediction-only and prediction-then-recommendation, the proposed
direct-recommendation method achieves satisfactory performance in different
metrics. Extensive experiments also demonstrate that the proposed ESGraph and
the recommendation model are more efficient in terms of computational
efficiency as well as saving drivers' on-street parking time
NLO QCD corrections to Single Top and W associated production at the LHC with forward detector acceptances
In this paper we study the Single Top and W boson associated photoproduction
via the main reaction at
the 14 TeV Large Hadron Collider (LHC) up to next-to-leading order (NLO) QCD
level assuming a typical LHC multipurpose forward detector. We use the
Five-Flavor-Number Schemes (5FNS) with massless bottom quark assumption in the
whole calculation. Our results show that the QCD NLO corrections can reduce the
scale uncertainty. The typical K-factors are in the range of 1.15 to 1.2 which
lead to the QCD NLO corrections of 15 to 20 correspond to the
leading-order (LO) predictions with our chosen parameters.Comment: 41pages, 12figures. arXiv admin note: text overlap with
arXiv:1106.2890 by other author
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