Noncyclic geometric changes of quantum states

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.Comment: Extended version, new title, journal reference adde

Manifestations of quantum holonomy in interferometry

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.Comment: Some changes, journal reference adde

Geometric phase distributions for open quantum systems

In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the environment and its coupling with the system yields a unique geometric phase distribution that applies even for mixed states, non-unitary dynamics, and non-cyclic evolutions.Comment: Some minor revisions, references update

Operational approach to the Uhlmann holonomy

We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements.Comment: Added material, references, and journal reference

Geometric phase for nonlinear coherent and squeezed state

The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated respectively. Moreover, some of their common properties are discussed respectively, such as gauge invariance, non-locality and non-linear effects. The non-linear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r -> \infinity, the limiting value of the geometric phase is also determined by non-linear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states maybe regarded as a geometric criterion

Noncyclic Pancharatnam phase for mixed state SU(2) evolution in neutron polarimetry

We have measured the Pancharatnam relative phase for spin-1/2 states. In a neutron polarimetry experiment the minima and maxima of intensity modulations, giving the Pancharatnam phase, were determined. We have also considered general SU(2) evolution for mixed states. The results are in good agreement with theory.Comment: 5 pages, 4 figures, to be published in Phys.Lett.

A general treatment of geometric phases and dynamical invariants

Based only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non-Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature

A controlled study of supplementation with essential amino acids and α-keto acids in the conservative management of patients with chronic renal failure

Art und Zusammensetzung einer optimalen eiweißarmen Ernährung für Patienten mit Niereninsuffizienz sind weiterhin umstritten. Die orale medikamentöse Behandlung mit essentiellen Aminosäuren oder α-Ketosäuren wird häufig empfohlen. Unsere Untersuchungen vergleichen nacheinander bei 15 ambulanten Patienten mit chronischem Nierenversagen (mittlere Kreatinin-Clearance 10,8 ml/min) unter einer eiweißarmen Ernährung von 0,57 g/kg Körpergewicht (40 g/70 kg) die Wirkung einer Substitution mit essentiellen Aminosäuren, danach die Substitution mit α-Ketosäuren gegenüber Plazebo. Der nachgewiesene Proteingehalt in der Nahrung betrug 0,55 g/kg, die Energiezufuhr 27 kcal/kg Körpergewicht, wie mehrfach Ernährungsprotokolle über jeweils 7 Tage bei den Patienten zeigen ließen. Nach einer Vorperiode von 6 Wochen nur unter diätetischen Maßnahmen erhielten alle Patienten zusätzlich 0,112 g essentielle Aminosäuren/kg Körpergewicht über 6 Wochen, danach in einer Doppelblinduntersuchung 0,105 g α-Ketosäuren/kg Körpergewicht im Vergleich gegenüber Plazebo, ebenfalls jeweils über 6 Wochen. Nüchtern-Blutuntersuchungen wurden für ein Standard-Laborwertprogramm, insbesondere für 15 Proteinmangelparameter, alle 3 Wochen durchgeführt, ferner anthropometrische und klinische Kontrollen. Die Laborwerte erbrachten keine Hinweise auf einen manifesten Proteinmangel. Die Therapie mit α-Ketosäuren erniedrigte die Phosphatspiegel signifikant (p<0,05). Dagegen konnten weder unter essentiellen Aminosäuren oder α-Ketosäuren andere für den Patienten wesentliche Effekte nachgewiesen werden. Deshalb erscheint uns eine Substitution mit essentiellen Aminosäuren oder Ketosäuren überflüssig bei Patienten mit einer chronischen Niereninsuffizienz, die sich in einem stabilen Stoffwechselgleichgewicht befinden und mit einer Eiweißzufuhr von 0,55 g/kg Körpergewicht behandelt werden. Oral therapy with essential amino acids (EAA) or α-keto acids (α-KA) has been recommended in patients with renal failure, but quality and quantity of optimal protein intake are still controversial. This study compares sequentially the effect of supplementation with EAA, and with α-KA versus placebo in 15 ambulatory patients with chronic renal failure (average creatinine clearance 10.8 ml/min), maintained on a protein diet of 0.57 g/kg body weight (40 g for a 70-kg patient). The actual dietary intake averaged 0.55 g protein/kg and 27 kcal/kg according to repeated 7-day dietary recordings. After a 6-week baseline period on this diet, all patients received additionally 0.112 g EAA/kg for 6 weeks followed by a double-blind cross-over study of 0.105 g α-KA/kg versus placebo supplementation for 6 weeks each. Fasting blood samples for multiple parameters, including 15 indicators for protein deficiency, as well as anthropometric and clinical data were evaluated every 3 weeks. Laboratory data revealed no indications of protein deficiency. Therapy with α-KA diminished serum phosphate concentration (p<0.05), however no other significant beneficial effects could be demonstrated during supplementation with either EAA or α-KA. Therefore, such supplementation to a 0.55-g/kg-protein diet appears superfluous in stable ambulatory patients with renal insufficiency.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41743/1/394_2005_Article_BF02020747.pd

A novel nonosteocytic regulatory mechanism of bone modeling

<div><p>Osteocytes, cells forming an elaborate network within the bones of most vertebrate taxa, are thought to be the master regulators of bone modeling, a process of coordinated, local bone-tissue deposition and removal that keeps bone strains at safe levels throughout life. Neoteleost fish, however, lack osteocytes and yet are known to be capable of bone modeling, although no osteocyte-independent modeling regulatory mechanism has so far been described. Here, we characterize a novel, to our knowledge, bone-modeling regulatory mechanism in a fish species (medaka), showing that although lacking osteocytes (i.e., internal mechanosensors), when loaded, medaka bones model in mechanically directed ways, successfully reducing high tissue strains. We establish that as in mammals, modeling in medaka is regulated by the <i>SOST</i> gene, demonstrating a mechanistic link between skeletal loading, <i>SOST</i> down-regulation, and intense bone deposition. However, whereas mammalian <i>SOST</i> is expressed almost exclusively by osteocytes, in both medaka and zebrafish (a species with osteocytic bones), <i>SOST</i> is expressed by a variety of nonosteocytic cells, none of which reside within the bone bulk. These findings argue that in fishes (and perhaps other vertebrates), nonosteocytic skeletal cells are both sensors and responders, shouldering duties believed exclusive to osteocytes. This previously unrecognized, <i>SOST</i>-dependent, osteocyte-independent mechanism challenges current paradigms of osteocyte exclusivity in bone-modeling regulation, suggesting the existence of multivariate feedback networks in bone modeling—perhaps also in mammalian bones—and thus arguing for the possibility of untapped potential for cell targets in bone therapeutics.</p></div