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A. Bohm

Publications and source records attributed to A. Bohm.

At least 19 recordsLinked to original sources
arXiv2010

Barred disks in dense environments

We investigate the properties of bright (MV <= -18) barred and unbarred disks in the Abell 901/902 cluster system at z~0.165 with the STAGES HST ACS survey. To identify and characterize bars, we use ellipse-fitting. We use visual classification, a Sersic cut, and a color cut to select disk galaxies, and find that the latter two methods miss 31% and 51%, respectively of disk galaxies identified through visual classification. This underscores the importance of carefully selecting the disk sample in cluster environments. However, we find that the global optical bar fraction in the clusters is ~30% regardless of the method of disk selection. We study the relationship of the optical bar fraction to host galaxy properties, and find that the optical bar fraction depends strongly on the luminosity of the galaxy and whether it hosts a prominent bulge or is bulgeless. Within a given absolute magnitude bin, the optical bar fraction increases for galaxies with no significant bulge component. Within each morphological type bin, the optical bar fraction increases for brighter galaxies. We find no strong trend (variations larger than a factor of 1.3) for the optical bar fraction with local density within the cluster between the core and virial radius (R ~ 0.25 to 1.2 Mpc). We discuss the implications of our results for the evolution of bars and disks in dense environments.

astro-ph.CO↗
arXiv2009

Interacting Galaxies in the A901/902 Supercluster with STAGES

We present a study of galaxy mergers and the influence of environment in the Abell 901/902 supercluster at z~0.165. We use HST ACS F606W data from the STAGES survey, COMBO-17, Spitzer 24um, and XMM-Newton X-ray data. Our analysis utilizes both a visual classification system, and quantitative CAS parameters to identify systems which show evidence of a recent or ongoing merger of mass ratio >1/10. Our results are: (1) After visual classification and minimizing the contamination from false projection pairs, we find that the merger fraction f_merge is 0.023+/-0.007. The estimated fractions of likely major mergers, likely minor mergers, and ambiguous cases are 0.01+/-0.004, 0.006+/-0.003, and 0.007+/-0.003, respectively. (2) The mergers lie outside the cluster core of radius R < 0.25 Mpc: the lack of mergers in the core is likely due to the large galaxy velocity dispersion in the core. Mergers populate the region (0.25 Mpc < R <= 2 Mpc) between the core and outskirt. In this region, the estimated frequency of mergers is similar to those seen at typical group overdensities. This suggests ongoing growth of the clusters via accretion of group and field galaxies. (3) We compare our observed merger fraction with those reported in other clusters and groups out to z~0.4. Existing data points on the merger fraction for L<= L* galaxies in clusters allow for a range of evolutionary scenarios. (4) The fraction of mergers, which lie on the blue cloud is 80%+/-18% versus 34%+/-7% for non-interacting galaxies, implying that interacting galaxies are preferentially blue. (5) The average SFR, based on UV or UV+IR data, is enhanced by a factor of ~1.5 to 2 in mergers compared to non-interacting galaxies. However, mergers in the clusters contribute only a small fraction (between 10% and 15%) of the total SFR density.(Abridged)

astro-ph.CO↗
arXiv2009

Barred Galaxies in the Abell 901/2 Supercluster with STAGES

We present a study of bar and host disk evolution in a dense cluster environment, based on a sample of ~800 bright (MV <= -18) galaxies in the Abell 901/2 supercluster at z~0.165. We use HST ACS F606W imaging from the STAGES survey, and data from Spitzer, XMM-Newton, and COMBO-17. We identify and characterize bars through ellipse-fitting, and other morphological features through visual classification. (1) We explore three commonly used methods for selecting disk galaxies. We find 625, 485, and 353 disk galaxies, respectively, via visual classification, a single component S'ersic cut (n <= 2.5), and a blue-cloud cut. In cluster environments, the latter two methods miss 31% and 51%, respectively, of visually-identified disks. (2) For moderately inclined disks, the three methods of disk selection yield a similar global optical bar fraction (f_bar-opt) of 34% +10%/-3%, 31% +10%/-3%, and 30% +10%/-3%, respectively. (3) f_bar-opt rises in brighter galaxies and those which appear to have no significant bulge component. Within a given absolute magnitude bin, f_bar-opt is higher in visually-selected disk galaxies that have no bulge as opposed to those with bulges. For a given morphological class, f_bar-opt rises at higher luminosities. (4) For bright early-types, as well as faint late-type systems with no evident bulge, the optical bar fraction in the Abell 901/2 clusters is comparable within a factor of 1.1 to 1.4 to that of field galaxies at lower redshifts (5) Between the core and the virial radius of the cluster at intermediate environmental densities, the optical bar fraction does not appear to depend strongly on the local environment density and varies at most by a factor of ~1.3. We discuss the implications of our results for the evolution of bars and disks in dense environments.

astro-ph.CO↗
arXiv2008

Quantal time asymmetry: mathematical foundation and physical interpretation

For a quantum theory that includes exponentially decaying states and Breit-Wigner resonances, which are related to each other by the lifetime-width relation $τ=\frac{\hbar}Γ$, where $τ$ is the lifetime of the decaying state and $Γ$ the width of the resonance, one has to go beyond the Hilbert space and beyond the Schwartz-Rigged Hilbert Space $Φ\subset\mathcal{H}\subsetΦ^\times$ of the Dirac formalism. One has to distinguish between prepared states, using a space $Φ_-\subset\mat hcal{H}$, and detected observables, using a space $Φ_+\subset\mathcal{H}$, where $-(+)$ refers to analyticity of the energy wave function in the lower (upper) complex energy semiplane. This differentiation is also justified by causality: A state needs to be prepared first, before an observable can be measured in it. The axiom that will lead to the lifetime-width relation is that $Φ_+$ and $Φ_-$ are Hardy spaces of the upper and lower semiplane, respectively. Applying this axiom to the relativistic case for the variable $\s=p_μp^μ$ leads to semigroup transformations into the forward light cone (Einstein causality) and a precise definition of resonance mass and width.

quant-ph↗
arXiv2008

Characterizing Barred Galaxies in the Abell 901/902 Supercluster

In dense clusters, higher densities at early epochs as well as physical processes, such as ram pressure stripping and tidal interactions become important, and can have direct consequences for the evolution of bars and their host disks. To study bars and disks as a function of environment, we are using the STAGES ACS HST survey of the Abell 901/902 supercluster (z~0.165), along with earlier field studies based the SDSS and the Ohio State University Bright Spiral Galaxy Survey (OSUBSGS). We explore the limitations of traditional methods for characterizing the bar fraction, and in particular highlight uncertainties in disk galaxy selection in cluster environments. We present an alternative approach for exploring the proportion of bars, and investigate the properties of bars as a function of host galaxy color, Sersic index, stellar mass, star formation rate (SFR), specific SFR, and morphology.

astro-ph↗
arXiv2007

Time Asymmetry in Quantum Physics - II. Experimental Demonstration Using a Single Ion

Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times. This provides the means of demonstrating the beginning of time of a semigroup evolution for a decaying state.

quant-ph↗
arXiv2005

Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm iε$ of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the $S$-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time $t=0$, a beginning of time. Its interpretation and observations are discussed in the last section.

quant-ph↗
arXiv2003

Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics

A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-``states'' of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schrödinger or Heisenberg) integrate to a semigroup evolution. Extending this new Hardy space axiom to a relativistic theory provides a relativistic theory of resonance scattering and decay with Born probablilities that fulfill Einstein causality and the exponential decay law.

quant-ph↗
arXiv2003

Representation of Semigroups in Rigged Hilbert Spaces: Subsemigroups of the Weyl-Heisenberg Group

This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are also investigated within the context of the results developed here.

math-ph↗
arXiv2003

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space.

math-ph↗
arXiv2003

On Einstein Causality and Time Asymmetry in Quantum Physics

A theorem of Hegerfeldt shows that if the spectrum of the Hamiltonian is bounded from below, then the propagation speed of certain probabilities does not have an upper bound. We prove a theorem analogous to Hegerfeldt's that appertains to asymmetric time evolutions given by a semigroup of operators. As an application, we consider a characterization of relativistic quasistable states by irreducible representations of the causal Poincare semigroup and study the implications of the new theorem for this special case.

quant-ph↗
arXiv2002

Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles

Relativistic resonances and decaying states are described by representations of Poincaré transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in- and out-scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several ``relativistic Breit-Wigner'' amplitudes, which represent the resonances per se. These Breit-Wigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincaré transformations into the forward light cone.

hep-th↗
arXiv2002

Time Asymmetric Quantum Theory - III. Decaying States and the Causal Poincare Semigroup

A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic Lippmann-Schwinger kets. These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of the Lippmann-Schwinger plane wave scattering states, form only a semigroup of Poincaré transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.

hep-th↗
arXiv2002

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.

quant-ph↗
arXiv2001

Rigged Hilbert Space Treatment of Continuous Spectrum

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrodinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave functions. They are also basis vectors that expand any physical wave function in a Dirac basis vector expansion. It is shown that an acceptable physical wave function must fulfill stronger conditions than just square integrability--the space of physical wave functions is not the whole Hilbert space but rather a dense subspace of the Hilbert space. We construct the position and energy representations of the Rigged Hilbert Space generated by the square barrier potential Hamiltonian. We shall also construct the unitary operator that transforms from the position into the energy representation. We shall see that in the energy representation the Dirac kets act as the antilinear Schwartz delta functional. In constructing the Rigged Hilbert Space of the square barrier potential, we will find a systematic procedure to construct the Rigged Hilbert Space of a large class of spherically symmetric potentials. The example of the square barrier potential will also make apparent that the natural framework for the solutions of a Schrodinger operator with continuous spectrum is the Rigged Hilbert Space rather than just the Hilbert space.

quant-ph↗
arXiv2001

Relativistic Gamow Vectors I Derivation from Poles of the S-Matrix

A state vector description for relativistic resonances is derived from the first order pole of the $j$-th partial $S$-matrix at the invariant square mass value $\sm_R=(m-i\Gamma/2)^2$ in the second sheet of the Riemann energy surface. To associate a ket, called Gamow vector, to the pole, we use the generalized eigenvectors of the four-velocity operators in place of the customary momentum eigenkets of Wigner, and we replace the conventional Hilbert space assumptions for the in- and out-scattering states with the new hypothesis that in- and out-states are described by two different Hardy spaces with complementary analyticity properties. The Gamow vectors have the following properties: - They are simultaneous generalized eigenvectors of the four velocity operators with real eigenvalues and of the self-adjoint invariant mass operator $M=(P_\mu P^\mu)^{1/2}$ with complex eigenvalue $\sqrt{\sm_R}$. - They have a Breit-Wigner distribution in the invariant square mass variable $\sm$ and lead to an exactly exponential law for the decay rates and probabilities.

hep-th↗
arXiv2000

Relativistic Gamow Vectors II

Motivated by the debate of possible definitions of mass and width of resonances for $Z$-boson and hadrons, we suggest a definition of unstable particles by ``minimally complex'' semigroup representations of the Poincaré group characterized by $(j,{\mathsf s}=(m-iΓ/2)^{2})$ in which the Lorentz subgroup is unitary. This definition, though decidedly distinct from those based on various renormalization schemes of perturbation theory, is intimately connected with the first order pole definition of the $S$-matrix theory in that the complex square mass $(m-iΓ/2)^{2}$ characterizing the representation of the Poincaré semigroup is exactly the position ${\mathsf s}_R$ at which the $S$-matrix has a simple pole. Wigner's representations $(j,m)$ are the limit case of the complex representations for $Γ=0$. These representations have generalized vectors (Gamow kets) which have, in addition to the $S$-matrix pole at ${\mathsf s}=(m-iΓ/2)^{2}$, all the other properties that heuristically the unstable states need to possess: a Breit-Wigner distribution in invariant square mass and a lifetime $τ=\frac{1}Γ$ defined by the exactly exponential law for the decay probability ${\cal P}(t)$ and rate $\dot{\cal P}(t)$ given by an exact Golden Rule which becomes Dirac's Golden Rule in the Born-approximation. In addition and unintended, they have an asymmetric time evolution.

hep-th↗