The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.
An intensive combination chemotherapy regimen supported by granulocyte colony-stimulating factor (G-CSF) was evaluated in adult T-cell leukemia/lymphoma (ATLL) patients in a multiinstitutional, cooperative study. Vincristine 1 mg/m2 i.v. day 1, Adriamycin 40 mg/m2 i.v. day 1, cyclophosphamide 400 mg/m2 i.v. day 1, prednisolone 40 mg/m2 i.v. days 1 to 3 and 8 to 10, etoposide 35 mg/m2 i.v. days 1 to 8, vindesine 2 mg/m2 i.v. day 8, ranimustine 50 mg/m2 i.v. day 8, mitoxantrone 7 mg/m2 i.v. day 8, and G-CSF 50 mg/m2 s.c. days 9 to 21 were given for 2 to 4 courses every 3 weeks to 83 patients with ATLL. Complete remission (CR) and partial remission (PR) were achieved in 35.8 and 38.3 percent, respectively, of 81 evaluable patients. The median survival of all patients was 8.5 months, with a predicted 3-year survival of 13.5 percent by the Kaplan-Meier method. The median duration of response was 7.6 months (range 0.2-42.7), and 13 patients were alive. Their median survival time was 29.1 months (range 19.2-44.7). In 67.6 percent of courses, white blood cell (WBC) nadirs were < 1.0 x 10(9)/L. Days required for the recovery of WBC from the nadir to > 1.0 x 10(9)/L were <5 days in 71.4 percent of the treatment courses. The G-CSF supported an intensified chemotherapy regimen for ATLL and yielded better response rate and longer survival compared to previous reports in Japan. Because duration of remission is still short, further studies of postremission therapy or other strategies are warranted.
The sign problem in QCD at finite temperature and density leads naturally to
the consideration of complex saddle points of the action or effective action.
The global symmetry $\mathcal{CK}$ of the finite-density action, where
$\mathcal{C}$ is charge conjugation and $\mathcal{K}$ is complex conjugation,
constrains the eigenvalues of the Polyakov loop operator $P$ at a saddle point
in such a way that the action is real at a saddle point, and net color charge
is zero. The values of $Tr_{F}P$ and $Tr_{F}P^{\dagger}$ at the saddle point,
are real but not identical, indicating the different free energy cost
associated with inserting a heavy quark versus an antiquark into the system. At
such complex saddle points, the mass matrix associated with Polyakov loops may
have complex eigenvalues, reflecting oscillatory behavior in color-charge
densities. We illustrate these properties with a simple model which includes
the one-loop contribution of gluons and massless quarks moving in a constant
Polyakov loop background. Confinement-deconfinement effects are modeled
phenomenologically via an added potential term depending on the Polyakov loop
eigenvalues. For sufficiently large $T$ and $\mu$, the results obtained reduce
to those of perturbation theory at the complex saddle point. These results may
be experimentally relevant for the CBM experiment at FAIR.Comment: 13 pages, 3 figures. Additional references and minor revision
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