<html><body><div id="zimbraEditorContainer" style="font-family: arial,helvetica,sans-serif; font-size: 12pt; color: #000000" class="2"><div><br></div><div><br></div><div data-marker="__HEADERS__"><br></div><br><div data-marker="__QUOTED_TEXT__"><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #000000"><div><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #000000;"><div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><strong><b><span style="font-size: 16pt; color: black;" lang="HR"><img src="cid:fb559ca8379da07816ebeb024a88bd13dae62179@zimbra" data-mce-src="cid:fb559ca8379da07816ebeb024a88bd13dae62179@zimbra"></span></b></strong></div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><p style="text-align: center; margin: 0px;" align="center"><b><span style="font-family: 'Century Gothic',sans-serif; color: #5f5f5f;" lang="EN-GB">Institut za fiziku, Bijenička cesta 46,</span></b></p><p style="text-align: center; margin: 0px;" align="center"><b><span style="font-family: 'Century Gothic',sans-serif; color: #5f5f5f;" lang="EN-GB">predavaonica u zgradi Mladen Paić</span></b></p><strong><b><span style="font-size: 14pt; font-family: 'Century Gothic',sans-serif; color: #993300;" lang="EN-GB">četvrtak, 5. srpnja 2018., u 11:00 sati</span></b><br></strong></div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><strong><b><span style="font-size: 14pt; font-family: 'Century Gothic',sans-serif; color: #993300;" lang="EN-GB"><br data-mce-bogus="1"></span></b></strong></div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><strong><b><span style="font-size: 14pt; font-family: 'Century Gothic',sans-serif; color: #993300;" lang="EN-GB">SEMINAR IF-a i ZCI-a <!--StartFragment-->QuantiXLie<!--EndFragment--> <br data-mce-bogus="1"></span></b></strong></div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><strong></strong> </div><div style="text-align: center;"><span style="color: #55913c; font-family: 'Times New Roman', serif;"><span style="font-size: 21.3333px;"><b>Numerical analytic continuation: answers to well-posed questions in ill-posed problem</b></span></span></div><div style="text-align: center;"><strong style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt;"><span style="font-size: 14pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB">dr. </span></strong><span style="font-family: 'Century Gothic', sans-serif;"><span style="font-size: 18.6667px;"><b>Andrey S. Mishchenko</b></span></span></div><div style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-align: center;"><b></b> </div><div style="text-align: center;"><span style="font-family: 'Century Gothic', sans-serif;"><span style="font-size: 14.6667px;"><b>RIKEN Center for Emergent Matter Science, Wako, Saitima, Japan</b></span></span></div><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 15px;"><span style="font-family: arial, helvetica, sans-serif;">We formulate [1] the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data.</span></p><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 15px;"><span style="font-family: arial, helvetica, sans-serif;">Combination of the stochastic optimization (SO) and consistent constraints (CC) method is used to obtain large number of independent solutions each describing the analytically continued spectrum with accuracy restricted by error-bars of the input data. We study different linear combinations of the independent solutions giving also valid final solution and look to how extent the final spectra can be different without compromising the error-bars of the input data. Such new philosophy (SOCC method) requiring the above post-processing of the analytic continuation data turns out to be crucial to reliably characterize the accuracy - or even ambiguity - of the output. We perform illustrative tests for spectra with a double-peak structure, where we critically examine which spectral properties are accessible and which ones are lost. We also show some important practical examples from science [2, 3] and technology [4].</span></p><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 15px;"><span style="font-family: arial, helvetica, sans-serif;"></span></p><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 15px;"><span style="font-family: arial, helvetica, sans-serif;">[1] O. Goulko, A. S. Mishchenko, L. Pollet, N. Prokof’ev, and B. Svistunov, Numerical analytic continuation: answers to well-posed questions, Phys. Rev. B <strong>95</strong>, 014102 (2017).</span></p><p style="margin: 15px;"><span style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;">[2] </span>O. Goulko, A. S. Mishchenko, N. Prokof'ev, and B. Svistunov, Dark continuum in the spectral function of the resonant Fermi polaron, Phys. Rev. A <strong>94</strong>, 051605(R) (2016).</p><p style="margin: 15px;"><span style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;">[3] </span>A. S. Mishchenko, N. Nagaosa, G. De Filippis, A. de Candia, and V. Cataudella, Mobility of Holstein Polaron at Finite Temperature: an Unbiased Approach, Phys. Rev. Lett. <strong>114</strong>, 146401 (2015).</p><p style="margin: 15px;"><span style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;">[4] </span>H. Matsui, A.S. Mishchenko, and T. Hasegawa: Distribution of localized states from the analysis of electron spin resonance spectra in organic transistors, Phys. Rev. Lett., <strong>104</strong>, 056602 (2010).</p><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 15px;"><span style="font-family: arial, helvetica, sans-serif;"></span></p><p style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin: 0px;"><b style="font-size: 12pt;"><span style="font-size: 12pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB"><b><span style="font-size: 11pt;" lang="EN-GB"> </span></b></span></b><span style="font-family: arial, helvetica, sans-serif;"></span></p></div><div style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-align: left;"><b><span style="font-size: 12pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB"><b><span style="font-size: 11pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB"> </span></b></span></b><b><span style="font-size: 12pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB"><b><span style="font-size: 11pt; font-family: 'Century Gothic',sans-serif;" lang="EN-GB">Voditelji seminara IF-a: <a href="mailto:hrvoje@ifs.hr" target="_blank">Hrvoje Skenderović</a> i <a href="mailto:damirs@ifs.hr" target="_blank">Damir Starešinić</a></span></b></span></b><br data-mce-bogus="1"></div></div><br></div></div><br><br></div></div></body></html>