TY - JOUR A1 - Öhberg, P. A1 - Surkov, E. L. A1 - Tittonen, I. A1 - Stenholm, Stig A1 - Wilkens, Martin A1 - Shlyapnikov, G. V. T1 - Low-energy elementary excitations of a trapped Bose-condensed gas N2 - We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation Y1 - 1997 ER - TY - JOUR A1 - Wilkens, Martin A1 - Weiss, Christoph T1 - Particle number fluctuations in an ideal Bose gas N2 - We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from theenvironment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of thegrand- canonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau-Ginzburg functional which - despite the non- interacting nature of the system - displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is base on the grand-canonical ensemble. We show that for an ideal Bose gas neither are the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir. Y1 - 1997 ER - TY - JOUR A1 - Wilkens, Martin A1 - Sütterlin, Sabine A1 - Weller, Nina A1 - Horn-Conrad, Antje A1 - Kampe, Heike A1 - Eckardt, Barbara A1 - Görlich, Petra A1 - Jäger, Sophie A1 - Zimmermann, Matthias A1 - Mitsch, Wolfgang T1 - Portal Wissen = Zeit BT - Das Forschungsmagazin der Universität Potsdam N2 - „Was ist also 'Zeit'?“ seufzt Augustinus von Hippo im 11. Buch seiner „Confessiones“ melancholisch, und fährt fort „Wenn mich niemand danach fragt, weiß ich es; will ich einem Fragenden es erklären, weiß ich es nicht.“ Auch heute, 1584 Jahre nach Augustinus, erscheint 'Zeit' immer noch rätselhaft. Abhandlungen über das Wesen der Zeit füllen Bibliotheken. Oder eben dieses Heft. Wesensfragen sind den modernen Wissenschaften allerdings fremd. Zeit ist – zumindest in der Physik – unproblematisch. „Time is defined so that Motion looks simple“ erkärt man kurz und trocken, und verabschiedet sich damit vom Augustinischen Rätsel oder der Newtonschen Vorstellung einer absoluten Zeit, deren mathematischen Fluss man durch irdische Instrumente eh immer nur näherungsweise erfassen kann. In der Alltagssprache, selbst in den Wissenschaften, reden wir zwar weiterhin vom Fluss der Zeit, aber Zeit ist schon lange keine natürliche Gegebenheit mehr. Zeit ist vielmehr ein konventioneller Ordnungsparameter für Änderung und Bewegung. Geordnet werden Prozesse, indem eine Klasse von Prozessen als Zählsystem dient, um andere Prozesse mit ihnen zu vergleichen und anhand der temporären Kategorien „vorher“, „während“ und „nachher“ anzuordnen. Zu Galileis Zeiten galt der eigene Pulsschlag als Zeitstandard für den Flug von Kanonenkugeln. Mit zunehmender Verfeinerung der Untersuchungsmethoden erschien das zu unpraktisch: Die Weg-Zeit-Diagramme frei fliegender Kanonenkugeln erweisen sich in diesem Standard ziemlich verwackelt, schlecht reproduzierbar, und keineswegs „simpel“. Heutzutage greift man zu Cäsium-Atomen. Demnach dauert ein Prozess eine Sekunde, wenn ein 133Cs-Atom genau 9 192 631 770 Schwingungen zwischen zwei sogenannten Hyperfeinzuständen des Grundzustands vollführt hat. Und ein Meter ist die Entfernung, die Licht im Vakuum in exakt 1/299 792 458 Sekunden zurücklegt. Glücklicherweise sind diese Daten im General Positioning System GPS hart kodiert, so dass der Nutzer sie nicht jedes Mal aufs Neue eingeben muss, wenn er wissen will, wo er ist. Aber schon morgen muss er sich vielleicht ein Applet runterladen, weil der Zeitstandard durch raffinierte Übergänge in Ytterbium ersetzt wurde. Der konventionelle Charakter des Zeitbegriffs sollte nicht dazu verführen zu glauben, alles sei irgendwie relativ und daher willkürlich. Die Beziehung eines Pulsschlags zu einer Atomuhr ist absolut, und genauso real, wie die Beziehung einer Sanduhr zum Lauf der Sonne. Die exakten Wissenschaften sind Beziehungswissenschaften. Sie handeln nicht vom Ding an sich, was Newton und Kant noch geträumt haben, sondern von Beziehungen – worauf schon Leibniz und später Mach hingewiesen haben. Kein Wunder, dass sich für andere Wissenschaften der physikalische Zeit-Standard als ziemlich unpraktisch erweist. Der Psychologie der Zeitwahrnehmung entnehmen wir – und jeder wird das bestätigen können – dass das gefühlte Alter durchaus verschieden ist vom physikalischen Alter. Je älter man ist, desto kürzer erscheinen einem die Jahre. Unter der einfachen Annahme, dass die gefühlte Dauer umgekehrt proportional zum physikalischen Alter ist, und man als Zwanzigjähriger ein physikalisches Jahr auch psychologisch als ein Jahr empfindet, ergibt sich der erstaunliche Befund, dass man mit 90 Jahren 90 Jahre ist. Und – bei einer angenommenen Lebenserwartung von 90 Jahren – mit 20 (bzw. 40) physikalischen Jahren bereits 67 (bzw. 82) Prozent seiner gefühlten Lebenszeit hinter sich hat. Bevor man angesichts der „Relativität von Zeit“ selbst in Melancholie versinkt, vielleicht die Fortsetzung des Eingangszitats von Augustinus: „Aber zuversichtlich behaupte ich zu wissen, dass es vergangene Zeit nicht gäbe, wenn nichts verginge, und nicht künftige Zeit, wenn nichts herankäme, und nicht gegenwärtige Zeit wenn nichts seiend wäre.“ Tja – oder mit Bob Dylan „The times they're a changing“. Ich wünsche Ihnen eine spannende Zeit bei der Lektüre dieser Ausgabe. Prof. Dr. Martin Wilkens Professor für Quantenoptik T3 - Portal Wissen: Das Forschungsmagazin der Universität Potsdam [Deutsche Ausgabe] - 02/2014 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-440842 SN - 2194-4237 IS - 02/2014 ER - TY - JOUR A1 - Wilkens, Martin A1 - Sütterlin, Sabine A1 - Kampe, Heike A1 - Eckardt, Barbara A1 - Jäger, Sophie A1 - Zimmermann, Matthias T1 - Portal Wissen = Time BT - The Research Magazine of the University of Potsdam N2 - “What then is time?”, Augustine of Hippo sighs melancholically in Book XI of “Confessions” and continues, “If no one asks me, I know; if I want to explain it to a questioner, I don’t know.” Even today, 1584 years after Augustine, time still appears mysterious. Treatises about the essence of time fill whole libraries – and this magazine. However, questions of essence are alien to modern sciences. Time is – at least in physics – unproblematic: “Time is defined so that motion looks simple”, briefly and prosaically phrased, waves goodbye to Augustine’s riddle and to the Newtonian concept of absolute time, whose mathematical flow can only be approximately recorded with earthly instruments anyway. In our everyday language and even in science we still speak of the flow of time but time has not been a natural condition for quite a while now. It is rather a conventional order parameter for change and movement. Processes are arranged by using a class of processes as a counting system in order to compare other processes and to organize them with the help of the temporary categories “before”, “during”, and “after”. During Galileo’s time one’s own pulse was seen as the time standard for the flight of cannon balls. More sophisticated examination methods later made this seem too impractical. The distance-time diagrams of free-flying cannon balls turned out to be rather imprecise, difficult to replicate, and in no way “simple”. Nowadays, we use cesium atoms. A process is said to take one second when a caesium-133 atom completes 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state. A meter is the length of the path travelled by light in a vacuum in exactly 1/299,792,458 of a second. Fortunately, these data are hard-coded in the Global Positioning System GPS so users do not have to reenter them each time they want to know where they are. In the future, however, they might have to download an app because the time standard has been replaced by sophisticated transitions to ytterbium. The conventional character of the time concept should not tempt us to believe that everything is somehow relative and, as a result, arbitrary. The relation of one’s own pulse to an atomic clock is absolute and as real as the relation of an hourglass to the path of the sun. The exact sciences are relational sciences. They are not about the thing-initself as Newton and Kant dreamt, but rather about relations as Leibniz and, later, Mach pointed out. It is not surprising that the physical time standard turned out to be rather impractical for other scientists. The psychology of time perception tells us – and you will all agree – that the perceived age is quite different from the physical age. The older we get the shorter the years seem. If we simply assume that perceived duration is inversely related to physical age and that a 20-year old also perceives a physical year as a psychological one, we come to the surprising discovery that at 90 years we are 90 years old. With an assumed life expectancy of 90 years, 67% (or 82%) of your felt lifetime is behind you at the age of 20 (or 40) physical years. Before we start to wallow in melancholy in the face of the “relativity of time”, let me again quote Augustine. “But at any rate this much I dare affirm I know: that if nothing passed there would be no past time; if nothing were approaching, there would be no future time; if nothing were, there would be no present time.” Well, – or as Bob Dylan sings “The times they are a-changin”. I wish you an exciting time reading this issue. Prof. Martin Wilkens Professor of Quantum Optics T3 - Portal Wissen: The research magazine of the University of Potsdam [Englische Ausgabe] - 02/2014 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-441497 SN - 2198-9974 IS - 02/2014 ER - TY - JOUR A1 - Wilkens, Martin A1 - Illuminati, Fabrizio A1 - Krämer, Meret T1 - Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble N2 - We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in power of the scattering length yields (Tc - Tc0)/Tc0=-0,93ap 1/3, where Tc0 is the transition temperature of the corresponding ideal Bose gas , a is the scattering length, and p is the particle number density. This is at vaiance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equevalence of statistical ensemble for the ideal Bose gas is thus confirm (at the lowestperturbative level) also in the presence of interactions. Y1 - 2000 ER - TY - JOUR A1 - Wilkens, Martin T1 - Quantum Phase of a Moving Dipole N2 - It is shown that a neutral particle with an electric dipole moment which moves in a magnetic field acquires a topological phase. This phase may be observed in atom or molecular interferometry. Y1 - 1998 ER - TY - JOUR A1 - Wilkens, Martin T1 - AS TIME GOES BY. Rythmizität Zyklizität - Kategorien zeitlicher Stukturierung JF - Zyklizität & Rhythmik: eine multidisziplinäre Vorlesungsreihe Y1 - 2020 SN - 978-3-86464-169-5 SP - 71 EP - 84 PB - trafo CY - Berlin ER - TY - JOUR A1 - Weiss, Christoph A1 - Wilkens, Martin T1 - Particle number counting statistics in ideal Bose gases N2 - We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence. Y1 - 1997 UR - http://epubs.osa.org/oearchive/source/2372.htm ER - TY - JOUR A1 - Volk, Benno A1 - Markert, Doreen A1 - Riejok, Henriette A1 - Dittberner, Jürgen A1 - Wanka, Johanna A1 - Wilkens, Martin A1 - Görtemaker, Manfred A1 - Regierer, Babette A1 - Steup, Martin A1 - Müller-Röber, Bernd A1 - Wernicke, Matthias A1 - Altenberger, Uwe A1 - Stölting, Erhard A1 - Ferý, Carolin A1 - Egenter, Peter A1 - Lenz, Claudia A1 - Jakubowski, Zuzanna A1 - Klötzer, Sylvia A1 - Krause, Michael A1 - Dietsch, Ulrich T1 - Portal = Vor der Präsidenten-Wahl: Erwartungen, Wünsche, Vorschläge BT - Die Potsdamer Universitätszeitung N2 - Aus dem Inhalt: - Vor der Präsidenten-Wahl: Erwartungen, Wünsche, Vorschläge - Der AStA in der Krise? - Über Satire und Macht in der DDR - Vom Fünf-Sterne-Koch zum Mensaleiter T3 - Portal: Das Potsdamer Universitätsmagazin - 04-05/2006 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-440005 SN - 1618-6893 IS - 04-05/2006 ER - TY - JOUR A1 - Tino, G. M. A1 - Cacciapuoti, L. A1 - Bongs, K. A1 - Bordé, Ch. J. A1 - Bouyer, P. A1 - Dittus, H. A1 - Ertmer, W. A1 - Görlitz, A. A1 - Inguscio, M. A1 - Landragin, A. A1 - Lemonde, P. A1 - Lämmerzahl, C. A1 - Peters, A. A1 - Rasel, E. A1 - Reichel, J. A1 - Salomon, C. A1 - Schiller, S. A1 - Schleich, W. A1 - Sengstock, K. A1 - Sterr, U. A1 - Wilkens, Martin T1 - Atom interferometers and optical atomic clocks : new quantum sensors for fundamental physics experiments in space N2 - We present projects for future space missions using new quantum devices based on ultracold atoms. They will enable fundamental physics experiments testing quantum physics, physics beyond the standard model of fundamental particles and interactions, special relativity, gravitation and general relativity. Y1 - 2007 ER - TY - JOUR A1 - Szameitat, Ulrike A1 - Wilkens, Martin A1 - Görlich, Petra A1 - Horn-Conrad, Antje A1 - Zimmermann, Matthias A1 - Reinhardt, Kristin A1 - Kampe, Heike A1 - Jäger, Heidi A1 - Wenzel, Anna Theresa A1 - Scholz, Jana T1 - Portal = Unter einem Dach: Lehrerbildung und Bildungsforschung BT - Das Potsdamer Universitätsmagazin N2 - Aus dem Inhalt: - Unter einem Dach: Lehrerbildung und Bildungsforschung - Waldweit - Nicht ohne Eisen und Schwefel T3 - Portal: Das Potsdamer Universitätsmagazin - 02/2015 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-440634 SN - 1618-6893 IS - 02/2015 ER - TY - JOUR A1 - Stenholm, Stig A1 - Wilkens, Martin T1 - Jumps in quantum theory N2 - In this paper we review the discussion about quantum jumps. We sketch the historical background before we present the recent revival of this problem originating in the field of atomic investigations. We present both the theoretical methods and their motivations, the relevance to experiments and an attempt at a preliminary discussion of the role of these developments in our fundamental understanding of quantum physics. Y1 - 1997 ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Effect of polarization entanglement in photon-photon scattering JF - Physical review : A, Atomic, molecular, and optical physics N2 - It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in quantum electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevA.95.012101 SN - 2469-9926 SN - 2469-9934 VL - 95 IS - 1 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light BT - the gravitational field of a laser pulse N2 - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 222 KW - electromagnetic radiation KW - general relativity KW - gravity KW - laser pulses KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-90553 ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light BT - the gravitational field of a laser pulse JF - New journal of physics : the open-access journal for physics N2 - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources. KW - gravity KW - general relativity KW - laser pulses KW - electromagnetic radiation KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/2/023009 SN - 1367-2630 VL - 18 SP - 1 EP - 16 PB - IOP Science CY - London ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light-the gravitational field of a laser pulse JF - NEW JOURNAL OF PHYSICS N2 - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources. KW - gravity KW - general relativity KW - laser pulses KW - electromagnetic radiation KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/2/023009 SN - 1367-2630 VL - 18 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - The effect of entanglement in gravitational photon-photon scattering JF - epl : a letters journal exploring the frontiers of physics N2 - The differential cross-section for gravitational photon-photon scattering calculated in perturbative quantum gravity is shown to depend on the degree of polarization entanglement of the two photons. The interaction between photons in the symmetric Bell state is stronger than between not entangled photons. In contrast, the interaction between photons in the anti-symmetric Bell state is weaker than between not entangled photons. The results are interpreted in terms of quantum interference, and it is shown how they fit into the idea of distance-dependent forces. Copyright (C) EPLA, 2016 Y1 - 2016 U6 - https://doi.org/10.1209/0295-5075/115/51002 SN - 0295-5075 SN - 1286-4854 VL - 115 SP - S12 EP - S13 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Räder, Andy A1 - Eisert, Jens A1 - Wilkens, Martin A1 - Schmidt, Robert A1 - Micka, Bettina A1 - Ostermeyer, Martin A1 - Zill, Rüdiger A1 - Baur, Jürgen A1 - Schmidt, Renate A1 - Leppin, Karin A1 - Slotowski, Agnes A1 - Resch-Esser, Ursula T1 - Portal = Albert Einsteins Erbe: Uni-Physiker forschen weiter BT - Die Potsdamer Universitätszeitung N2 - Aus dem Inhalt: - Albert Einsteins Erbe: Uni-Physiker forschen weiter - Uni-Studiengang im europäischen Exzellenzprogramm - Sternenstaubsammler - Mit Einfallsreichtum gegen den Trend T3 - Portal: Das Potsdamer Universitätsmagazin - 01-03/2005 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439846 SN - 1618-6893 IS - 01-03/2005 ER - TY - JOUR A1 - Rzazewski, Kazimierz A1 - Goral, K. A1 - Cirone, M. A. A1 - Wilkens, Martin T1 - Bose-Einstein Condensation of two interacting particles N2 - We investigate the notion of Bose-Einstein condensation of interacting particles. The definition of the condensate is based on the existence of the dominant eigenvalue of the single-particle density matrix. The statistical properies and the characteristics temperature are computed exactly in the soluble models of two interacting atoms. Y1 - 2001 ER - TY - JOUR A1 - Raetzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light: The emission of counter-propagating laser pulses from an atom JF - Physical review : D, Particles, fields, gravitation, and cosmology Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevD.95.084008 SN - 2470-0010 SN - 2470-0029 VL - 95 PB - American Physical Society CY - College Park ER -