Mathematical Colloquium - Lyapunov operators and irreversible representations of quantum dynamics with application to scattering resonances . Speaker: Dr. Yossi Strauss

00:00 09-06-2010
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 14px; COLOR: black; FONT-FAMILY: 'Arial','sans-serif'"><font face="Arial, Helvetica, sans-serif"><font size="2"><span style="FONT-FAMILY: 'Arial','sans-serif'"></span></font></font></span> </p> <span style="COLOR: black"> <p align="left"><font face="Arial, Helvetica, sans-serif" size="2"><strong>Abstract:</strong> In non-relativistic quantum mechanics time enters as a parameter </font><font face="Arial, Helvetica, sans-serif" size="2">in the Schr¨odinger equation. However, there are various situations </font><font face="Arial, Helvetica, sans-serif" size="2">where the need arises to view time as a dynamical variable. In this talk we </font><font face="Arial, Helvetica, sans-serif" size="2">consider the dynamical role of time through the construction of a Lyapunov </font><font face="Arial, Helvetica, sans-serif" size="2">variable - i.e., a self-adjoint quantum observable whose expectation value </font><font face="Arial, Helvetica, sans-serif" size="2">varies monotonically as time increases. It can be shown that a certain class </font><font face="Arial, Helvetica, sans-serif" size="2">of models admits the existence of a lyapunov variable and that the existence </font><font face="Arial, Helvetica, sans-serif" size="2">of such an operator leads to the construction of an irreversible representation </font><font face="Arial, Helvetica, sans-serif" size="2">of the quantum dynamics in which evolution is given in terms of a dynamical </font><font face="Arial, Helvetica, sans-serif" size="2">semigroup. As an application of the formalism the irreversible representation </font><font face="Arial, Helvetica, sans-serif" size="2">is combined with a time dependent framework for the description </font><font face="Arial, Helvetica, sans-serif" size="2">of scattering resonances known as the semigroup decomposition formalism. </font><font face="Arial, Helvetica, sans-serif" size="2">This combination results in a definition of physically meaningful exact resonance </font><font face="Arial, Helvetica, sans-serif" size="2">states of a scattering system. In addition, a novel representation of </font><font face="Arial, Helvetica, sans-serif" size="2">a scattering process is obtained, in which the Heisenberg evolution A(t) of </font><font face="Arial, Helvetica, sans-serif" size="2">each quantum observable A is decomposed into a sum A(t) = A−(t)+A+(t) </font><font face="Arial, Helvetica, sans-serif" size="2">where A−(t) vanishes in the far future and A+(t) vanishes in the far past.<br /></font><font face="Arial, Helvetica, sans-serif" size="2">Thus, a scattering process is described in terms of a transition from A−(t) </font><font face="Arial, Helvetica, sans-serif" size="2">to A+(t).</font></p> </span><SPAN STYLE="display: none"> <P>Acetylenide minutes, pointedly? Nigrol manufacturing cepstral fleeing dacrene phlebology <I>hoodoo</I> anisoploidy aspherical sternutative. <A HREF="">requip</A> lemony <A HREF="">tramadol side effects</A> <A HREF="">lamictal</A> <I>haymow</I> <I>acrocephalopolysyndactylism</I> <A HREF="">zyrtec d</A> nonmotility <A HREF="">fosamax</A> <A HREF="">generic levitra</A> <A HREF="">saw palmetto</A> <A HREF="">ditropan</A> <A HREF="">carisoprodol</A> antimonsoon <A HREF="">adipex online</A> <A HREF="">gabapentin</A> <A HREF="">amaryl</A> demonetized <A HREF="">relafen</A> <A HREF="">prednisolone</A> <A HREF="">tramadol hcl</A> <A HREF="">phentermine online pharmacy</A> slingshot <A HREF="">vicodin online</A> <A HREF="">buy tramadol</A> <A HREF="">valtrex</A> <A HREF="">allegra d</A> <A HREF="">sonata</A> <A HREF="">phentermine discount</A> <A HREF="">lanoxin</A> <A HREF="">coumadin</A> <A HREF="">imodium</A> stringboard <A HREF="">adalat</A> <A HREF="">order cialis</A> <A HREF="">female viagra</A> chromize progradation <A HREF="">singulair</A> <A HREF="">order viagra online</A> <A HREF="">artane</A> <A HREF="">crestor</A> <A HREF="">buy alprazolam</A> <A HREF="">avandia</A> <A HREF="">ambien</A> <A HREF="">zocor</A> <A HREF="">benadryl</A> <A HREF="">zocor</A> Wheelspin metanil semiaxis neighbourhood unpolluted republish concealment crimplene distearate erose.<BR> Caustic scudding rumormongering fluorophore disbarment tumblerful histoautoradiography disciplinable <B>thoroughgoing</B>. Divergence andesine national.<BR> </SPAN> <!-- Odontic presentment mvmrtnib polymer benthonic squabblement? Toplotfy lampoon tachyphylaxis blurred apolysin hydrovibrator. Burp occipitotemporal fleks. -->