13,481 research outputs found
Spectroscopic studies in open quantum systems
The spectroscopic properties of an open quantum system are determined by the
eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the
Hamiltonian H_0 of the corresponding closed system and a non-Hermitian
correction term W arising from the interaction via the continuum of decay
channels. The eigenvalues E_R of H are complex. They are the poles of the
S-matrix and provide both the energies and widths of the states. We illustrate
the interplay between Re(H) and Im(H) by means of the different interference
phenomena between two neighboured resonance states. Level repulsion along the
real axis appears if the interaction is caused mainly by Re(H) while a
bifurcation of the widths appears if the interaction occurs mainly due to
Im(H). We then calculate the poles of the S-matrix and the corresponding
wavefunctions for a rectangular microwave resonator with a scatter as a
function of the area of the resonator as well as of the degree of opening to a
guide. The calculations are performed by using the method of exterior complex
scaling. Re(W) and Im(W) cause changes in the structure of the wavefunctions
which are permanent, as a rule. At full opening to the lead, short-lived
collective states are formed together with long-lived trapped states. The
wavefunctions of the short-lived states at full opening to the lead are very
different from those at small opening. The resonance picture obtained from the
microwave resonator shows all the characteristic features known from the study
of many-body systems in spite of the absence of two-body forces. The poles of
the S-matrix determine the conductance of the resonator. Effects arising from
the interplay between resonance trapping and level repulsion along the real
axis are not involved in the statistical theory.Comment: The six jpg files are not included in the tex-fil
Fast readout of a single Cooper-pair box using its quantum capacitance
We have fabricated a single Cooper-pair box (SCB) together with an on-chip
lumped element resonator. By utilizing the quantum capacitance of the SCB, its
state can be read out by detecting the phase of a radio-frequency (rf) signal
reflected off the resonator. The resonator was optimized for fast readout. By
studying quasiparticle tunneling events in the SCB, we have characterized the
performance of the readout and found that we can perform a single shot parity
measurement in approximately 50 ns. This is an order of magnitude faster than
previously reported measurements.Comment: 7 pages, 5 figure
Influence of surface roughness on superhydrophobicity
Superhydrophobic surfaces, with liquid contact angle theta greater than 150
degree, have important practical applications ranging from self-cleaning window
glasses, paints, and fabrics to low-friction surfaces. Many biological
surfaces, such as the lotus leaf, have hierarchically structured surface
roughness which is optimized for superhydrophobicity through natural selection.
Here we present a molecular dynamics study of liquid droplets in contact with
self-affine fractal surfaces. Our results indicate that the contact angle for
nanodroplets depends strongly on the root-mean-square surface roughness
amplitude but is nearly independent of the fractal dimension D_f of the
surface.Comment: 5 Pages, 6 figures. Minimal changes with respect to the previous
versio
Molecular dynamics study of contact mechanics: contact area and interfacial separation from small to full contact
We report a molecular dynamics study of the contact between a rigid solid
with a randomly rough surface and an elastic block with a flat surface. We
study the contact area and the interfacial separation from small contact (low
load) to full contact (high load). For small load the contact area varies
linearly with the load and the interfacial separation depends logarithmically
on the load. For high load the contact area approaches to the nominal contact
area (i.e., complete contact), and the interfacial separation approaches to
zero. The present results may be very important for soft solids, e.g., rubber,
or for very smooth surfaces, where complete contact can be reached at moderate
high loads without plastic deformation of the solids.Comment: 4 pages,5 figure
Contact mechanics with adhesion: Interfacial separation and contact area
We study the adhesive contact between elastic solids with randomly rough,
self affine fractal surfaces. We present molecular dynamics (MD) simulation
results for the interfacial stress distribution and the wall-wall separation.
We compare the MD results for the relative contact area and the average
interfacial separation, with the prediction of the contact mechanics theory of
Persson. We find good agreement between theory and the simulation results. We
apply the theory to the system studied by Benz et al. involving polymer in
contact with polymer, but in this case the adhesion gives only a small
modification of the interfacial separation as a function of the squeezing
pressure.Comment: 5 pages, 4 figure
Eisenstein series and automorphic representations
We provide an introduction to the theory of Eisenstein series and automorphic
forms on real simple Lie groups G, emphasising the role of representation
theory. It is useful to take a slightly wider view and define all objects over
the (rational) adeles A, thereby also paving the way for connections to number
theory, representation theory and the Langlands program. Most of the results we
present are already scattered throughout the mathematics literature but our
exposition collects them together and is driven by examples. Many interesting
aspects of these functions are hidden in their Fourier coefficients with
respect to unipotent subgroups and a large part of our focus is to explain and
derive general theorems on these Fourier expansions. Specifically, we give
complete proofs of the Langlands constant term formula for Eisenstein series on
adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic
spherical Whittaker function associated to unramified automorphic
representations of G(Q_p). In addition, we explain how the classical theory of
Hecke operators fits into the modern theory of automorphic representations of
adelic groups, thereby providing a connection with some key elements in the
Langlands program, such as the Langlands dual group LG and automorphic
L-functions. Somewhat surprisingly, all these results have natural
interpretations as encoding physical effects in string theory. We therefore
also introduce some basic concepts of string theory, aimed toward
mathematicians, emphasising the role of automorphic forms. In particular, we
provide a detailed treatment of supersymmetry constraints on string amplitudes
which enforce differential equations of the same type that are satisfied by
automorphic forms. Our treatise concludes with a detailed list of interesting
open questions and pointers to additional topics which go beyond the scope of
this book.Comment: 326 pages. Detailed and example-driven exposition of the subject with
highlighted applications to string theory. v2: 375 pages. Substantially
extended and small correction
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