Elementary solution to the time-independent quantum navigation problem

A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realizes a required quantum process or task, under the influence of a prevailing ‘background’ Hamiltonian that cannot be manipulated. When the task is to transform one quantum state into another, finding the solution in closed form to the problem is nontrivial even in the case of timeindependent Hamiltonians. An elementary solution, based on trigonometric analysis, is found here when the Hilbert space dimension is two. Difficulties arising from generalizations to higher-dimensional systems are discussed

Entropy and Temperature of a Quantum Carnot Engine

It is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic expansion. It is shown that the existence of such a bath leads to equilibrium quantum states that maximise the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that allow one to define the temperature of the energy bath.Comment: 4 pages, 1 figur

LABOR LAW - COVERAGE UNDER FAIR LABOR STANDARDS ACT OF SERVICE EMPLOYEES OF LOFT BUILDING WHOSE TENANTS ARE ENGAGED IN COMMERCE

Defendant was a lessor of a loft building, portions of which were occupied by clothing manufacturers who shipped their products into interstate commerce. As part of its obligation under the lease, the defendant offered service and maintenance of the building, employing for that purpose elevator operators, watchmen, firemen, an engineer, a carpenter and his helper, and a porter. Defendant appealed from an injunction prohibiting it from further violating the wage provisions of the Fair Labor Standards Act of 1938. The circuit court of appeals affirmed the judgment of the district court granting the injunction. Held, on certiorari, one justice dissenting, that the decision of the circuit court of appeals be affirmed. The employees were engaged in the production of goods for commerce and did not fall within the statutory exemption for service establishments. Kirschbaum v. Walling, (U. S. 1942) 62 S. Ct. 1116

CONSTITUTIONAL LAW-STATE APPORTIONMENT FOR CONGRESSIONAL ELECTIONS-JUSTICIABILITY OF ISSUE

Petitioners, three qualified Illinois voters, filed a proceeding in a United States district court composed of three judges, seeking a determination under the Federal Declaratory Judgment Act that the 1901 State Apportionment Act of Illinois was in violation of the Fourteenth Amendment and Article I of the Constitution, in that it denied to citizens of the United States the equal and unabridged right to vote for Congressmen. On direct appeal to the Supreme Court of a dismissal of the petition by the lower court, the complaint alleged that the statute apportioning the State of Illinois was void in that it failed to provide for compactness of territory and approximate equality of population, with the result of a substantial disparity between the effectiveness of petitioners\u27 votes in their heavily populated districts as compared to those of voters living in more sparsely populated districts. Held, affirmed. The complaint was properly dismissed for want of equity: due regard for the effective workings of our Government revealed this issue to be of a peculiarly political nature and therefore not meet for judicial determination. Justices Douglas and Murphy joined in Justice Black\u27s dissent. Colegrove v. Green, (U.S. 1946) 66 S. Ct. 1198

TRUSTS-WHERE SETTLOR HAS PREVIOUSLY MADE AN ABSOLUTE GIFT OF CORPUS TO TRUSTEE-SELF DECLARATION OF TRUST

In 1930 plaintiff received certain shares of stock from his uncle by way of outright gift. Seven months later, in order to decrease inheritance taxes at the time of the death of the donee, a declaration of trust was prepared and executed by the original donor as settlor, and indorsed by the donee as Trustee, to evidence his acceptance of the Trusts herein expressed, at which time the donee surrendered the certificate of shares originally given him and was issued a new certificate as trustee. Plaintiff now sues for an annulment of the instrument. Held, the document was void as a deed of trust, since the settlor had no property interest in the shares nothing passed to the donee as trustee, or to the beneficiaries. Nor was a trust created in donee\u27s own property in favor of the beneficiaries. Coleman v. Coleman, (Wash. 1946) 17I P. (2d) 691

CONSTITUTIONAL LAW-TRIAL BY MILITARY COMMISSION OF ENEMY COMBATANT AFTER CESSATION OF HOSTILITIES-SCOPE OF INQUIRY IN HABEAS CORPUS PROCEEDINGS

Petitioner, the Commanding General of the Fourteenth Army Group of the Imperial Japanese Army in the Philippine Islands, surrendered to and became a prisoner of war of the United States Army Forces in Baguio, Philippine Islands on September 3, 1945. By order of respondent, petitioner was served, on September 25, with a charge setting forth a violation of the law of war. On October 8 petitioner, after pleading not guilty to the charge, was held for trial before a military commission of five Army officers appointed by General Styer, and a bill of particulars was filed by the prosecution specifying sixty-four items. On October 29, the day of commencement of trial, a supplemental bill of particulars was filed, containing fifty-nine additional specifications, a copy of which had been given to the defense three days earlier. On December 7, the commission pronounced petitioner guilty and sentenced him to death by hanging. Appeal was made to the Supreme Court of the United States for leave to file a petition for writs of habeas corpus and prohibition, and also a petition for certiorari to review an order of the Supreme Court of the Commonwealth of the Philippines denying petitioner\u27s application to that court for writs of habeas corpus and prohibition. Petitioner claimed that his detention for trial by the military commission was without lawful authority or jurisdiction and raised the following questions: (1) whether the military commission was lawfully created, and whether such a tribunal could be convened after the cessation of hostilities to try him for a violation of the law of war; (2) whether the charge, that as commander he had failed to control the troops under his command by permitting them to commit atrocities, in fact stated a violation of the law of war; (3) whether he was denied a fair trial in violation of the due process clause of the Fifth Amendment because the order governing the procedure of the commission, which authorized the admission of certain types of evidence, was contrary to the Articles of War which prescribe the procedure before military tribunals, And violated the provisions of the Geneva Convention of 1929, which stipulate that a prisoner of war shall be entitled to trial by the same courts and according to the same procedure as in the case of persons belonging to the armed forces of the detaining power; and (4) whether the commission was without jurisdiction because of the failure to give advance notice of his trial to the neutral power representing the interests of Japan as a belligerent, as required by the Geneva Convention of 1929. Held, both petitions denied, since it appeared that the order convening the commission was a lawful order, that the commission was lawfully constituted, that petitioner was charged with a violation of the law of war, and that the commission had authority to proceed with the trial, and in doing so did not violate any military, statutory or constitutional ground (Justices Murphy and Rutledge dissenting). Application of Yamashita, and Yamashita v. Styer, Commanding General, U.S. Army Forces, Western Pacific, (U.S. 1945) 66 S.Ct. 340.