The Quantum Mechanics Solver uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics. All of these problems are based on actual physical examples, even if sometimes the mathematical structure of the models under consideration is simplified intentionally in order to get hold of the physics more rapidly. The new edition features new themes, such as the progress in measuring neutrino oscillations, quantum boxes, the quantum thermometer etc. Secondly, it includes a brief summary on the basics of quantum mechanics and the formalism we use. Finally, the problems under three main themes: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems.

IT ALL BEGINS IN THIS STUNNING FIRST NOVEL!
Born in rage, a killer before she left the amniotic sac, the Lady Desdemona is a genetically enhanced vampire, a death goddess with three thousand years of bloody history tucked under her belt - and no signs of slowing down.
In the festering city of Golgotha Falls high technology meshes uncomfortably with ancient ritual - here there are doorways that exist in the very fabric of space and time, software programmes that can overwrite a man's personality, monsters born on the dark side of physics and demons that bypass the laws of physics altogether. Golgotha Falls is a city that caters to every unholy fetish and every sordid desire, a technological wonderland with a dark, toxic underbelly.

This collection of stories touches upon many genres: Normed Trek is a clever and witty Alice-in-Wonderland-type narrative set in the realm of mathematical analysis, The Cantor Trilogy is a dystopia about the consequences of relying upon computer-based mathematical proofs, In Search of Future Time bears the flavor of Tales from Arabian Nights set in the future, and – last but not least - Murder on the Einstein Express is a short, non-technical primer on probabilities and modern classical physics, disguised as a detective story.
Written primarily for an audience with some background or a strong interest in mathematics, physics and computer science (in particular artificial intelligence), these stories explore the boundaries between science and fiction in a refreshingly unconventional fashion. In the Afterthoughts the author provides some further insights and annotations

A Business Week, New York Times Business, and USA Today Bestseller"Ambitious and readable . . . an engaging introduction to the oddsmakers, whom Bernstein regards as true humanists helping to release mankind from the choke holds of superstition and fatalism." -The New York Times"An extraordinarily entertaining and informative book." -The Wall Street Journal"A lively panoramic book . . . Against the Gods sets up an ambitious premise and then delivers on it." -Business Week"Deserves to be, and surely will be, widely read." -The Economist"[A] challenging book, one that may change forever the way people think about the world." -Worth"No one else could have written a book of such central importance with so much charm and excitement." -Robert Heilbroner author, The Worldly Philosophers"With his wonderful knowledge of the history and current manifestations of risk, Peter Bernstein brings us Against the Gods. Nothing like it will come out of the financial world this year or ever. I speak carefully: no one should miss it." -John Kenneth Galbraith Professor of Economics Emeritus, Harvard UniversityIn this unique exploration of the role of risk in our society, Peter Bernstein argues that the notion of bringing risk under control is one of the central ideas that distinguishes modern times from the distant past. Against the Gods chronicles the remarkable intellectual adventure that liberated humanity from oracles and soothsayers by means of the powerful tools of risk management that are available to us today."An extremely readable history of risk." -Barron's"Fascinating . . . this challenging volume will help you understand the uncertainties that every investor must face." -Money"A singular achievement." -Times Literary Supplement"There's a growing market for savants who can render the recondite intelligibly-witness Stephen Jay Gould (natural history), Oliver Sacks (disease), Richard Dawkins (heredity), James Gleick (physics), Paul Krugman (economics)-and Bernstein would mingle well in their company." -The Australian

We present in this paper a quantitative method for defining void size in
large-scale structure based on percolation threshold density. Beginning with
two-dimensional gravitational clustering simulations smoothed to the threshold
of nonlinearity, we perform percolation analysis to determine the large scale
structure. The resulting objective definition of voids has a natural scaling
property, is topologically interesting, and can be applied immediately to redshift
surveys.

We present in this paper a quantitative method for defining void size in
large-scale structure based on percolation threshold density. Beginning with
two-dimensional gravitational clustering simulations smoothed to the threshold
of nonlinearity, we perform percolation analysis to determine the large scale
structure. The resulting objective definition of voids has a natural scaling
property, is topologically interesting, and can be applied immediately to redshift
surveys.

A gravitational lens model of the radio quasar B1422+231 is presented which can account
for the image arrangement and approximately for the relative magnifications. The locations
of the principal lensing mass and a more distant secondary mass concentration were predicted
and subsequently luminous galaxies were found at these locations. This argues against the
existence of substantial numbers of “dark” galaxies. The model suggests that if the compact
radio source is intrinsically superluminal then the observed component motions may be as large
as
∼ 100
c with image B moving in the opposite direction to images A and C. The prospects for
a measuring the Hubble constant from a model incorporating lens galaxy locations, compact
radio source expansion speeds and radio time delays, if and when these are measured, are
briefly assessed.

We consider the production of gravitons in an inflationary cosmology by ap-
proximating each epoch of change in the equation of state as sudden, from which a
simple analytic graviton mode function has been derived. We use this mode func-
tion to compute the graviton spectral energy density and the tensor-induced cosmic
microwave background anisotropy.

Various theoretical uncertainties in the standard solar model and in the
Mikheyev-Smirnov-Wolfenstein (MSW) analysis are discussed. It is shown
that two methods of estimating the solar neutrino flux uncertainties are
equivalent:

In the non-critical string framework that we have proposed recently, the time t is identified
with a dynamical local renormalization group scale, the Liouville mode, and behaves as
a statistical evolution parameter, flowing irreversibly from an infrared fixed point - which
we conjecture to be a topological string phase - to an ultraviolet one - which corresponds
to a static critical string vacuum. When applied to a toy two-dimensional model of space-
time singularities, this formalism yields an apparent renormalization of the velocity of
light, and a t-dependent form of the uncertainty relation for position and momentum of a
test string. We speculate within this framework on a stringy alternative to conventional
field-theoretical inflation, and the decay towards zero of the cosmological constant in a
maximally-symmetric space.

Using an analytical model for the string network we show that the
kurtosis of cosmic microwave background (CMB) temperature gradi-
ent maps is a good statistic to distinguish between the cosmic string
model and inflationary models of structure formation.

We employ N{body/3D gas dynamic simulations of the formation of galaxy clusters
to determine whether cluster X{ray morphologies can be used as cosmological constraints.
Conrming the analytic expectations of Richstone, Loeb, & Turner, we demonstrate that
cluster evolution is sensitive to the cosmological model in which the clusters form. We
further show that evolutionary dierences are echoed in the gross morphological features of
the cluster X{ray emission.

We examine the possibility that gamma-ray bursts arise from sources in the Oort comet
cloud, basing most of our arguments on accepted models for the formation and spatial
distribution of the cloud

Good statistics for measuring large-scale structure in the Universe must be able
to distinguish between different models of structure formation. In this paper, two
and three dimensional “counts in cell” statistics and a new “discrete genus statis-
tic” are applied to toy versions of several popular theories of structure formation:
random phase cold dark matter model, cosmic string models, and global texture
scenario. All three statistics appear quite promising in terms of differentiating
between the models.

In this letter we propose a physical explanation for recently reported correla-
tions between pairs of close and antipodal gamma-ray bursts from publicly avail-
able BATSE catalogue. Our model is based on the cosmological scenario in which
bursters are located at cosmological distances of order of 0.5–2 Gpc. Observed dis-
tribution of gamma-ray bursts strongly suports this assumption. If so gamma-ray
bursts may provide a very good probe for investigating the topological structure
of the Universe. We notice that correlation between antipodal events may in fact
indicate that we live in the so called Ellis’ small universe which has Friedman-
Roberston-Walker metric structure and nontrivial topology.

Although Potent purports to use only radial velocities in retrieving the potential ve-
locity eld of galaxies, the derivation of transverse components is implicit in the smoothing
procedures. Thus the possibility of using nonradial line integrals to derive the velocity
eld arises. In the case of inhomogeneous distributions of galaxies, the optimal path for
integration need not be radial, and can be obtained by using max-
ow algorithms. In this
paper we present the results of using Dijkstra's algorithm to obtain this optimal path and
velocity eld.

We investigate the eect of using dierent distance estimators on the recovery of the
peculiar velocity eld of galaxies using Potent. An inappropriate choice of distance
estimator will give rise to spurious
ows. We discuss methods of minimising these biases
and the levels of accuracy required of distance estimators to retrieve velocity elds to a
given standard.

Methods for inferring the velocity eld from the peculiar velocity data are described and applied
to old and newer data. Inhomogeneous Malmquist bias and ways to avoid it are discussed and
utilized. We infer that these biases are probably important in interpreting the data.

Studies of inclined rings inside galaxy potentials have mostly considered the in-
uence of self{gravity and viscous dissipation separately. In this study, we construct
models of highly-inclined (\polar") rings in an external potential including both self{
gravity and dissipation due to a drag force.

We describe an analytic distribution function of a nite, oblate stellar system that is
useful for the practical modelling of dark halos. The function is determined by lowering
Evans's (1993) distribution function of a
attened, cored isothermal system in analogy
to the lowering of the singular, isothermal sphere in the denition of the King (1966)
model

A pseudo-Nambu-Goldstone boson, with a potential of the form V (φ) = Λ4
[1 + cos(φ/f)],
can naturally give rise to an epoch of inflation in the early universe (Freese, Frieman, and Olinto
1990). The potential is naturally flat (as required by microwave background limits on the
amplitude of density fluctuations), without any fine-tuning. Successful inflation can be achieved
if f ∼ mpl and Λ ∼ mGUT . Such mass scales arise in particle physics models with a large gauge
group that becomes strongly interacting at a scale ∼ Λ, e.g., as can happen in the hidden sector
of superstring theories.

We study nonlinear wave phenomena in self-gravitating fluid systems, with a partic-
ular emphasis on applications to molecular clouds. This paper presents analytical results
for one spatial dimension

We have performed a series of high resolution N-body experiments on a Connection
Machine CM-5 in order to simulate the formation of galaxy clusters gravitationally
dominated by a massive dark background.

The recent detection of microlensing of stars of LMC by compact objects in
the halo of our galaxy
1
−
2
suggests that our galaxy is surrounded by a non-
luminous halo made of compact objects with mass of about (0.03−0.5)M⊙.

We use high resolution dissipationless N-body simulations to examine the spatial dis-
tribution of galaxy clusters on large scales. The Standard CDM model and two of its
main competitors,

We use ensembles of high-resolution CDM simulations to investigate the shape and
amplitude of the two point correlation function of rich clusters. The standard scale-
invariant CDM model with
= 1 provides a poor description of the clustering mea-
sured from the APM rich cluster redshift survey, which is better tted by models with
more power at large scale

Most of the mass density in the Universe—and in the halo of our own
galaxy—exists in the form of dark matter. Overall, the contribution of lu-
minous matter (in stars) to the mass density of the Universe is less than
1%;