A note on the Zassenhaus product formula

We provide a simple method for the calculation of the terms c_n in the Zassenhaus product $e^{a+b}=e^a e^b \prod_{n=2}^{\infty} e^{c_n}$ for non-commuting a and b. This method has been implemented in a computer program. Furthermore, we formulate a conjecture on how to translate these results into nested commutators. This conjecture was checked up to order n=17 using a computer

Mitschrift der Vorlesung zu Mechanische Wärmetheorie von Jacob Johann Weyrauch durch Ludwig Kieninger

MITSCHRIFT DER VORLESUNG ZU MECHANISCHE WÄRMETHEORIE VON JACOB JOHANN WEYRAUCH DURCH LUDWIG KIENINGER Mitschriften und Skripte von Vorlesungen an der Technischen Hochschule und Universität Stuttgart (-) Mitschrift der Vorlesung zu Mechanische Wärmetheorie von Jacob Johann Weyrauch durch Ludwig Kieninger (Bd. 22, 1896) (1) Einband (-) Verzeichniss (-) Mechanische Wärmetheorie. [Wintersemester 1896/97] (1) I. Abschnitt / Erhaltung der Energie (1) II. Abschnitt / Wärme und Arbeit (34) III. Abschnitt / Termodynamische Maschinen (75) IV. Abschnitt / Gase (90) V. Abschnitt / Heissluftmaschinen (139) VI. Abschnitt / Gasmaschine (167) VII. Abschnitt / Von den gesättigten Dämpfen (205) VIII. Abschnitt / Über die Druckzunahme in abgepressten Dampfkessel (235) Aërostatik und Aërodynamik. Sommersemester 1897 (311) I. Abschnitt / Vom [Gleichgewicht gasförmiger] Körper (311) II. Abschnitt / Strömende Bewegung von Gasen und Dämpfen (336) Tabellen (425) Farbinformation (-) Einband (-

Mitschrift der Vorlesung zu Mechanische Wärmetheorie von Jacob [Johann] Weyrauch durch Hans Herrmann 1902/03

MITSCHRIFT DER VORLESUNG ZU MECHANISCHE WÄRMETHEORIE VON JACOB [JOHANN] WEYRAUCH DURCH HANS HERRMANN 1902/03 Mitschriften und Skripte von Vorlesungen an der Technischen Hochschule und Universität Stuttgart (-) Mitschrift der Vorlesung zu Mechanische Wärmetheorie von Jacob [Johann] Weyrauch durch Hans Herrmann 1902/03 (Bd. 21, 1902-1903) (3) Einband (-) Mechanische Wärmetheorie (-) Inhaltsverzeichnis (-) Einleitung (1) I Abschnitt: Erster Hauptsatz; Erhaltung der Energie (3) II Abschnitt: Zweiter Satz; Wärme und Arbeit (44) III Abschnitt: Wärmemotoren im Allgemeinen (104) IV Abschnitt: Von den Gasen; Einleitung (139) V Abschnitt: Luftmaschinen (219) VI Abschnitt: Über Explosions- & Vertretungsmaschinen (299) Zeitschriftenartikel: Diesels rationeller Wärmemotor von Rudolf Diesel (359) Zeitschriftenartikel: Diesels rationeller Wärmemotor von M. Schröter (371) Alphabetisches Sachregister (393) Zeitschrift des Vereines deutscher Ingenieure / Nr. 38, Band XXXXIII. (406) Amerikanische Maschinen und Maschinenanlagen von C. Regenbogen (406) Beharrungsvermögen von Kondensatoren von F. J. Weifs (412) Ueber den Ausfluss von Gasen und Dämpfen bei abnehmendem Druck und bei abnehmendem Volumen von Jacob [Johann] Weyrauch (419) Doppelte Auslegerbohrmaschine, ausgeführt von der Maschinenfabrik Oerlikon (423) Sitzungsbericht der Bezirksvereine (425) Bücherschau (428) Zeitschriftenschau (430) Rundschau (434) Patentbericht (435) Zuschriften an die Redaktion (437) Zeitschrift des Vereines deutscher Ingenieure / Nr. 39, Band XXXXIII (438) Anforderungen der Elektrotechnik an die Kraftmaschinen von Rob. M. Friese (438) Eine moderne Maschinenfabrik (445) Ueber den Ausfluss von Gasen und Dämpfen bei abnehmendem Druck und bei abnehmendem Volumen von Jacob [Johann] Weyrauch (457) Sitzungsberichte der Bezirksvereine (460) Zeitschriftenschau (463) Rundschau (467) Patentbericht (470) Angelegenheiten des Vereines (471) Farbinformation (-) Einband (-

The large system asymptotics of persistent currents in mesoscopic quantum rings

We consider a one-dimensional mesoscopic quantum ring filled with spinless electrons and threaded by a magnetic flux, which carries a persistent current at zero temperature. The interplay of Coulomb interactions and a single on-site impurity yields a non-trivial dependence of the persistent current on the size of the ring. We determine numerically the asymptotic power law for systems up to 32000 sites for various impurity strengths and compare with predictions from Bethe Ansatz solutions combined with Bosonization. The numerical results are obtained using an improved functional renormalization group (fRG) method. We apply the density matrix renormalization group (DMRG) and exact diagonalization methods to benchmark the fRG calculations. We use DMRG to study the persistent current at low electron concentrations in order to extend the validity of our results to quasi-continuous systems. We briefly comment on the quality of calculated fRG ground state energies by comparison with exact DMRG data.Comment: REVTex, 12 pages, 12 figs, accepted in Phys. Rev.

Transport through correlated quantum dots: An investigation using the functional renormalization group

Calculations using the (exact) fermionic functional renormalization group are usually truncated at the second order of the corresponding hierarchy of coupled ordinary differential equations. We present a method for the systematic determination of higher order vertex functions. This method is applied to a study of transport properties of various correlated quantum dot systems. It is shown that for large Coulomb correlations higher order vertex functions cannot be neglected, and a static approximation is insufficient.Comment: 10 figures, accepted by Phys. Rev.

Reduction of quantum noise in optical interferometers using squeezed light

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90{\deg} to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R.Barak and Y.Ben-Aryeh, J.Opt.Soc.Am.B25(361)2008]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.Comment: 8 pages, 1 figur

Flow Equation for Supersymmetric Quantum Mechanics

We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.Comment: 24 pages, 8 figures, references added, typos correcte

Theoretical study of the dynamic structure factor of superfluid 4He

We study the dynamic structure factor $S(\vec{q},\omega)$ of superfluid 4He at zero temperature in the roton momentum region and beyond using field-theoretical Green's function techniques. We start from the Gavoret-Nozi\`{e}res two-particle propagator and introduce the concept of quasiparticles. We treat the residual (weak) interaction between quasiparticles as being local in coordinate space and weakly energy dependent. Our quasiparticle model explicitly incorporates the Bose-Einstein condensate. A complete formula for the dynamic susceptibility, which is related to $S (\vec{q},\omega)$, is derived. The structure factor is numerically calculated in a self-consistent way in the special case of a momentum independent interaction between quasiparticles. Results are compared with experiment and other theoretical approaches.Comment: 17 pages, 16 figure

Radiative decays of decuplet hyperons

We calculate the radiative decay widths of decuplet hyperons in a chiral constituent quark model including electromagnetic exchange currents between quarks. Exchange currents contribute significantly to the E2 transition amplitude, while they largely cancel for the M1 transition amplitude. Strangeness suppression of the radiative hyperon decays is found to be weakened by exchange currents. Differences and similarities between our results and other recent model predictions are discussed.Comment: 11 pages, 1 eps figure, revtex, accepted for publication in Phys. Rev.

Comment on “Unique Translation between Hamiltonian Operators and Functional Integrals”

A comment on the letter by Tim Gollisch and Christof Wetterich, Phys. Rev. Lett. 86, 1 (2001).Michael Weyrauch, and Andreas W. Schreibe